%------------------------------------------------------------------------------
% File     : ITP049_4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : llist.ax [Gau19]
%          : HL4049_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  821 ( 318 unt; 317 typ;   0 def)
%            Number of atoms       :  978 ( 696 equ)
%            Maximal formula atoms :   15 (   1 avg)
%            Number of connectives :  492 (  18   ~;  25   |; 158   &)
%                                         (  95 <=>; 196  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :   22 (   3 avg)
%            Number of types       :   22 (  21 usr)
%            Number of type conns  :  251 ( 170   >;  81   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  295 ( 295 usr; 126 con; 0-3 aty)
%            Number of variables   : 1884 (1801   !;  83   ?;1884   :)
% 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: $tType ).

tff(mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: $tType ).

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

tff(mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: $tType ).

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

tff(tyop_2Ellist_2Ellist,type,
    tyop_2Ellist_2Ellist: d > d ).

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

tff(tyop_2Enum_2Enum,type,
    tyop_2Enum_2Enum: d ).

tff(tyop_2Eoption_2Eoption,type,
    tyop_2Eoption_2Eoption: d > d ).

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

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

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

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

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

tff(c_2Epair_2E_23_23_2E0,type,
    c_2Epair_2E_23_23_2E0: u ).

tff(c_2Epair_2E_23_23_2E2,type,
    c_2Epair_2E_23_23_2E2: ( du * 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_2Epair_2E_2C_2E0,type,
    c_2Epair_2E_2C_2E0: u ).

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

tff(c_2Earithmetic_2E_2D_2E0,type,
    c_2Earithmetic_2E_2D_2E0: u ).

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

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

tff(c_2Enum_2E0_2E0,type,
    c_2Enum_2E0_2E0: u ).

tff(c_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_2E1,type,
    c_2Emin_2E_3D_2E1: du > u ).

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

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

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

tff(c_2Emin_2E_40_2E0,type,
    c_2Emin_2E_40_2E0: u ).

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

tff(c_2Elist_2EAPPEND_2E0,type,
    c_2Elist_2EAPPEND_2E0: u ).

tff(c_2Elist_2EAPPEND_2E1,type,
    c_2Elist_2EAPPEND_2E1: du > 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_2Earithmetic_2EBIT2_2E0,type,
    c_2Earithmetic_2EBIT2_2E0: u ).

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

tff(c_2Epred__set_2ECHOICE_2E0,type,
    c_2Epred__set_2ECHOICE_2E0: u ).

tff(c_2Epred__set_2ECHOICE_2E1,type,
    c_2Epred__set_2ECHOICE_2E1: du > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

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

tff(c_2Elist_2ECONS_2E0,type,
    c_2Elist_2ECONS_2E0: u ).

tff(c_2Elist_2ECONS_2E1,type,
    c_2Elist_2ECONS_2E1: du > u ).

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

tff(c_2Epred__set_2EDIFF_2E0,type,
    c_2Epred__set_2EDIFF_2E0: u ).

tff(c_2Epred__set_2EDIFF_2E2,type,
    c_2Epred__set_2EDIFF_2E2: ( du * du ) > u ).

tff(c_2Elist_2EDROP_2E0,type,
    c_2Elist_2EDROP_2E0: u ).

tff(c_2Elist_2EDROP_2E2,type,
    c_2Elist_2EDROP_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_2Epred__set_2EEMPTY_2E0,type,
    c_2Epred__set_2EEMPTY_2E0: u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Epair_2EFST_2E0,type,
    c_2Epair_2EFST_2E0: u ).

tff(c_2Earithmetic_2EFUNPOW_2E0,type,
    c_2Earithmetic_2EFUNPOW_2E0: u ).

tff(c_2Earithmetic_2EFUNPOW_2E3,type,
    c_2Earithmetic_2EFUNPOW_2E3: ( du * du * du ) > u ).

tff(c_2Elist_2EGENLIST_2E0,type,
    c_2Elist_2EGENLIST_2E0: u ).

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

tff(c_2Epred__set_2EGSPEC_2E0,type,
    c_2Epred__set_2EGSPEC_2E0: u ).

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

tff(c_2Elist_2EHD_2E0,type,
    c_2Elist_2EHD_2E0: u ).

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

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

tff(c_2Eoption_2EIS__SOME_2E0,type,
    c_2Eoption_2EIS__SOME_2E0: u ).

tff(c_2Eoption_2EIS__SOME_2E1,type,
    c_2Eoption_2EIS__SOME_2E1: du > u ).

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

tff(c_2Ellist_2ELAPPEND_2E0,type,
    c_2Ellist_2ELAPPEND_2E0: u ).

tff(c_2Ellist_2ELAPPEND_2E2,type,
    c_2Ellist_2ELAPPEND_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELCONS_2E0,type,
    c_2Ellist_2ELCONS_2E0: u ).

tff(c_2Ellist_2ELCONS_2E2,type,
    c_2Ellist_2ELCONS_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELDROP_2E0,type,
    c_2Ellist_2ELDROP_2E0: u ).

tff(c_2Ellist_2ELDROP_2E1,type,
    c_2Ellist_2ELDROP_2E1: du > u ).

tff(c_2Ellist_2ELDROP_2E2,type,
    c_2Ellist_2ELDROP_2E2: ( du * 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_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

tff(c_2Ebool_2ELET_2E2,type,
    c_2Ebool_2ELET_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELFILTER_2E0,type,
    c_2Ellist_2ELFILTER_2E0: u ).

tff(c_2Ellist_2ELFILTER_2E2,type,
    c_2Ellist_2ELFILTER_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELFINITE_2E0,type,
    c_2Ellist_2ELFINITE_2E0: u ).

tff(c_2Ellist_2ELFINITE_2E1,type,
    c_2Ellist_2ELFINITE_2E1: du > u ).

tff(c_2Ellist_2ELFLATTEN_2E0,type,
    c_2Ellist_2ELFLATTEN_2E0: u ).

tff(c_2Ellist_2ELFLATTEN_2E1,type,
    c_2Ellist_2ELFLATTEN_2E1: du > u ).

tff(c_2Ellist_2ELGENLIST_2E0,type,
    c_2Ellist_2ELGENLIST_2E0: u ).

tff(c_2Ellist_2ELGENLIST_2E2,type,
    c_2Ellist_2ELGENLIST_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELHD_2E0,type,
    c_2Ellist_2ELHD_2E0: u ).

tff(c_2Ellist_2ELHD_2E1,type,
    c_2Ellist_2ELHD_2E1: du > u ).

tff(c_2Ellist_2ELLENGTH_2E0,type,
    c_2Ellist_2ELLENGTH_2E0: u ).

tff(c_2Ellist_2ELLENGTH_2E1,type,
    c_2Ellist_2ELLENGTH_2E1: du > u ).

tff(c_2Ellist_2ELMAP_2E0,type,
    c_2Ellist_2ELMAP_2E0: u ).

tff(c_2Ellist_2ELMAP_2E2,type,
    c_2Ellist_2ELMAP_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELNIL_2E0,type,
    c_2Ellist_2ELNIL_2E0: u ).

tff(c_2Ellist_2ELNTH_2E0,type,
    c_2Ellist_2ELNTH_2E0: u ).

tff(c_2Ellist_2ELNTH_2E1,type,
    c_2Ellist_2ELNTH_2E1: du > u ).

tff(c_2Ellist_2ELNTH_2E2,type,
    c_2Ellist_2ELNTH_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELPREFIX_2E0,type,
    c_2Ellist_2ELPREFIX_2E0: u ).

tff(c_2Ellist_2ELPREFIX_2E2,type,
    c_2Ellist_2ELPREFIX_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELREPEAT_2E0,type,
    c_2Ellist_2ELREPEAT_2E0: u ).

tff(c_2Ellist_2ELREPEAT_2E1,type,
    c_2Ellist_2ELREPEAT_2E1: du > u ).

tff(c_2Ellist_2ELTAKE_2E0,type,
    c_2Ellist_2ELTAKE_2E0: u ).

tff(c_2Ellist_2ELTAKE_2E2,type,
    c_2Ellist_2ELTAKE_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELTL_2E0,type,
    c_2Ellist_2ELTL_2E0: u ).

tff(c_2Ellist_2ELTL_2E1,type,
    c_2Ellist_2ELTL_2E1: du > u ).

tff(c_2Ellist_2ELTL__HD_2E0,type,
    c_2Ellist_2ELTL__HD_2E0: u ).

tff(c_2Ellist_2ELTL__HD_2E1,type,
    c_2Ellist_2ELTL__HD_2E1: du > u ).

tff(c_2Ellist_2ELUNFOLD_2E0,type,
    c_2Ellist_2ELUNFOLD_2E0: u ).

tff(c_2Ellist_2ELUNFOLD_2E1,type,
    c_2Ellist_2ELUNFOLD_2E1: du > u ).

tff(c_2Ellist_2ELUNFOLD_2E2,type,
    c_2Ellist_2ELUNFOLD_2E2: ( du * du ) > u ).

tff(c_2Ellist_2ELUNZIP_2E0,type,
    c_2Ellist_2ELUNZIP_2E0: u ).

tff(c_2Ellist_2ELUNZIP_2E1,type,
    c_2Ellist_2ELUNZIP_2E1: du > u ).

tff(c_2Ellist_2ELZIP_2E0,type,
    c_2Ellist_2ELZIP_2E0: u ).

tff(c_2Ellist_2ELZIP_2E1,type,
    c_2Ellist_2ELZIP_2E1: du > u ).

tff(c_2Earithmetic_2EMOD_2E0,type,
    c_2Earithmetic_2EMOD_2E0: u ).

tff(c_2Earithmetic_2EMOD_2E2,type,
    c_2Earithmetic_2EMOD_2E2: ( du * du ) > u ).

tff(c_2Elist_2ENIL_2E0,type,
    c_2Elist_2ENIL_2E0: u ).

tff(c_2Eoption_2ENONE_2E0,type,
    c_2Eoption_2ENONE_2E0: u ).

tff(c_2Elist_2ENULL_2E0,type,
    c_2Elist_2ENULL_2E0: u ).

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

tff(c_2Earithmetic_2ENUMERAL_2E0,type,
    c_2Earithmetic_2ENUMERAL_2E0: u ).

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

tff(c_2Eoption_2EOPTION__BIND_2E0,type,
    c_2Eoption_2EOPTION__BIND_2E0: u ).

tff(c_2Eoption_2EOPTION__BIND_2E2,type,
    c_2Eoption_2EOPTION__BIND_2E2: ( du * du ) > u ).

tff(c_2Eoption_2EOPTION__JOIN_2E0,type,
    c_2Eoption_2EOPTION__JOIN_2E0: u ).

tff(c_2Eoption_2EOPTION__JOIN_2E1,type,
    c_2Eoption_2EOPTION__JOIN_2E1: du > u ).

tff(c_2Eoption_2EOPTION__MAP_2E0,type,
    c_2Eoption_2EOPTION__MAP_2E0: u ).

tff(c_2Eoption_2EOPTION__MAP_2E2,type,
    c_2Eoption_2EOPTION__MAP_2E2: ( du * du ) > u ).

tff(c_2Eprim__rec_2EPRE_2E0,type,
    c_2Eprim__rec_2EPRE_2E0: u ).

tff(c_2Epair_2ESND_2E0,type,
    c_2Epair_2ESND_2E0: u ).

tff(c_2Eoption_2ESOME_2E0,type,
    c_2Eoption_2ESOME_2E0: u ).

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

tff(c_2Epred__set_2ESUBSET_2E0,type,
    c_2Epred__set_2ESUBSET_2E0: u ).

tff(c_2Epred__set_2ESUBSET_2E2,type,
    c_2Epred__set_2ESUBSET_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_2Elist_2ETAKE_2E0,type,
    c_2Elist_2ETAKE_2E0: u ).

tff(c_2Elist_2ETAKE_2E2,type,
    c_2Elist_2ETAKE_2E2: ( du * du ) > u ).

tff(c_2Eoption_2ETHE_2E0,type,
    c_2Eoption_2ETHE_2E0: u ).

tff(c_2Eoption_2ETHE_2E1,type,
    c_2Eoption_2ETHE_2E1: du > u ).

tff(c_2Elist_2ETL_2E0,type,
    c_2Elist_2ETL_2E0: u ).

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

tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
    c_2Ebool_2ETYPE__DEFINITION_2E0: u ).

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

tff(c_2Epair_2EUNCURRY_2E0,type,
    c_2Epair_2EUNCURRY_2E0: u ).

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

tff(c_2Epred__set_2EUNION_2E0,type,
    c_2Epred__set_2EUNION_2E0: u ).

tff(c_2Epred__set_2EUNION_2E2,type,
    c_2Epred__set_2EUNION_2E2: ( du * du ) > u ).

tff(c_2Earithmetic_2EZERO_2E0,type,
    c_2Earithmetic_2EZERO_2E0: u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

tff(c_2Eset__relation_2Edomain_2E0,type,
    c_2Eset__relation_2Edomain_2E0: u ).

tff(c_2Eset__relation_2Edomain_2E1,type,
    c_2Eset__relation_2Edomain_2E1: du > u ).

tff(c_2Ellist_2Eevery_2E0,type,
    c_2Ellist_2Eevery_2E0: u ).

tff(c_2Ellist_2Eevery_2E2,type,
    c_2Ellist_2Eevery_2E2: ( du * du ) > u ).

tff(c_2Ellist_2Eexists_2E0,type,
    c_2Ellist_2Eexists_2E0: u ).

tff(c_2Ellist_2Eexists_2E2,type,
    c_2Ellist_2Eexists_2E2: ( du * du ) > u ).

tff(c_2Eset__relation_2Efinite__prefixes_2E0,type,
    c_2Eset__relation_2Efinite__prefixes_2E0: u ).

tff(c_2Eset__relation_2Efinite__prefixes_2E2,type,
    c_2Eset__relation_2Efinite__prefixes_2E2: ( du * du ) > u ).

tff(c_2Ellist_2EfromList_2E0,type,
    c_2Ellist_2EfromList_2E0: u ).

tff(c_2Ellist_2EfromList_2E1,type,
    c_2Ellist_2EfromList_2E1: du > u ).

tff(c_2Elist_2EisPREFIX_2E0,type,
    c_2Elist_2EisPREFIX_2E0: u ).

tff(c_2Elist_2EisPREFIX_2E2,type,
    c_2Elist_2EisPREFIX_2E2: ( du * du ) > u ).

tff(c_2Eset__relation_2Elinear__order_2E0,type,
    c_2Eset__relation_2Elinear__order_2E0: u ).

tff(c_2Eset__relation_2Elinear__order_2E2,type,
    c_2Eset__relation_2Elinear__order_2E2: ( du * du ) > u ).

tff(c_2Ellist_2Elinear__order__to__list__f_2E0,type,
    c_2Ellist_2Elinear__order__to__list__f_2E0: u ).

tff(c_2Ellist_2Elinear__order__to__list__f_2E1,type,
    c_2Ellist_2Elinear__order__to__list__f_2E1: du > u ).

tff(c_2Ellist_2Ellength__rel_2E0,type,
    c_2Ellist_2Ellength__rel_2E0: u ).

tff(c_2Ellist_2Ellength__rel_2E2,type,
    c_2Ellist_2Ellength__rel_2E2: ( du * du ) > u ).

tff(c_2Ellist_2Ellist__abs_2E0,type,
    c_2Ellist_2Ellist__abs_2E0: u ).

tff(c_2Ellist_2Ellist__abs_2E1,type,
    c_2Ellist_2Ellist__abs_2E1: du > u ).

tff(c_2Ellist_2Ellist__rep_2E0,type,
    c_2Ellist_2Ellist__rep_2E0: u ).

tff(c_2Ellist_2Ellist__rep_2E1,type,
    c_2Ellist_2Ellist__rep_2E1: du > u ).

tff(c_2Ellist_2Ellist__rep_2E2,type,
    c_2Ellist_2Ellist__rep_2E2: ( du * du ) > u ).

tff(c_2Ellist_2Elrep__ok_2E0,type,
    c_2Ellist_2Elrep__ok_2E0: u ).

tff(c_2Ellist_2Elrep__ok_2E1,type,
    c_2Ellist_2Elrep__ok_2E1: du > u ).

tff(c_2Eset__relation_2Eminimal__elements_2E0,type,
    c_2Eset__relation_2Eminimal__elements_2E0: u ).

tff(c_2Eset__relation_2Eminimal__elements_2E2,type,
    c_2Eset__relation_2Eminimal__elements_2E2: ( du * du ) > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

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

tff(c_2Eoption_2Eoption__CASE_2E0,type,
    c_2Eoption_2Eoption__CASE_2E0: u ).

tff(c_2Eoption_2Eoption__CASE_2E3,type,
    c_2Eoption_2Eoption__CASE_2E3: ( du * du * du ) > u ).

tff(c_2Epair_2Epair__CASE_2E0,type,
    c_2Epair_2Epair__CASE_2E0: u ).

tff(c_2Epair_2Epair__CASE_2E2,type,
    c_2Epair_2Epair__CASE_2E2: ( du * du ) > u ).

tff(c_2Eset__relation_2Erange_2E0,type,
    c_2Eset__relation_2Erange_2E0: u ).

tff(c_2Eset__relation_2Erange_2E1,type,
    c_2Eset__relation_2Erange_2E1: du > u ).

tff(c_2Eset__relation_2Errestrict_2E0,type,
    c_2Eset__relation_2Errestrict_2E0: u ).

tff(c_2Eset__relation_2Errestrict_2E2,type,
    c_2Eset__relation_2Errestrict_2E2: ( du * du ) > u ).

tff(c_2Ellist_2EtoList_2E0,type,
    c_2Ellist_2EtoList_2E0: u ).

tff(c_2Ellist_2EtoList_2E1,type,
    c_2Ellist_2EtoList_2E1: 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 * mono_2Etyop_2Emin_2Ebool ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Earithmetic_2EBIT1_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Earithmetic_2EBIT2_2E0,type,
    mono_2Ec_2Earithmetic_2EBIT2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

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

tff(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 ).

tff(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: ( mono_2Etyop_2Emin_2Ebool * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Earithmetic_2EMOD_2E0,type,
    mono_2Ec_2Earithmetic_2EMOD_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Earithmetic_2EMOD_2E2,type,
    mono_2Ec_2Earithmetic_2EMOD_2E2: ( mono_2Etyop_2Enum_2Enum * mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum ).

tff(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 * mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ) > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eprim__rec_2EPRE_2E0,type,
    mono_2Ec_2Eprim__rec_2EPRE_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 ).

tff(mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,type,
    mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).

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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 > u ).

tff(i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 > u ).

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

tff(i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 > 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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 ).

tff(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29 ).

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

tff(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,type,
    j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29: du > mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29 ).

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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0) ) ).

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

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

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

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

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0_2E0) ) ).

tff(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),V0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(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(ij_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),V0_2E0)))) = s(tyop_2Eoption_2Eoption(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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

tff(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29] : ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_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(ji_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0))) = V0_2E0 ) ).

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

tff(arityeq2_2Ec_2Epair_2E_23_23_2E2_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Epair_2E_23_23_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),c_2Epair_2E_23_23_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_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_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,A_27a))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) ) ).

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

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),c_2Epair_2E_2C_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(A_27a,X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Epair_2E_2C_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(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(arityeq1_2Ec_2Emin_2E_3D_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

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

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

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Elist_2EAPPEND_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = 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))) ) ).

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

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

tff(arityeq1_2Ec_2Epred__set_2ECHOICE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a),c_2Epred__set_2ECHOICE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0),s(tyop_2Ellist_2Ellist(A_27a),X2_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0),s(tyop_2Ellist_2Ellist(A_27b),X2_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0,X1_2E0,X2_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X0_2E0),X1_2E0),X2_2E0) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X2_2E0))) ) ).

tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E1(s(A_27a,X0_2E0))) = 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))) ) ).

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(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E1(s(A_27b,X0_2E0))) = 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))) ) ).

tff(arityeq1_2Ec_2Elist_2ECONS_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E1(s(A_27c,X0_2E0))) = 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))) ) ).

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

tff(arityeq2_2Ec_2Elist_2EDROP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_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_2Elist_2EDROP_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_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(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Earithmetic_2EFUNPOW_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),c_2Earithmetic_2EFUNPOW_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X2_2E0))) ) ).

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

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

tff(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epred__set_2EGSPEC_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),X0_2E0))) ) ).

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

tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Eoption_2EIS__SOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Ebool),c_2Eoption_2EIS__SOME_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELAPPEND_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELAPPEND_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELCONS_2E0),s(A_27a,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,X0_2E0),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27c))),c_2Ellist_2ELCONS_2E0),s(A_27c,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2EA_27d,axiom,
    ! [A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELCONS_2E2(s(A_27d,X0_2E0),s(tyop_2Ellist_2Ellist(A_27d),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27d),tyop_2Ellist_2Ellist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27d),tyop_2Ellist_2Ellist(A_27d))),c_2Ellist_2ELCONS_2E0),s(A_27d,X0_2E0))),s(tyop_2Ellist_2Ellist(A_27d),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)))),c_2Ellist_2ELCONS_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27c_29,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27c),X0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),X1_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)))),c_2Ellist_2ELCONS_2E0),s(tyop_2Ellist_2Ellist(A_27c),X0_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27d_29,axiom,
    ! [A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27d),X0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),X1_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27d),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)))),c_2Ellist_2ELCONS_2E0),s(tyop_2Ellist_2Ellist(A_27d),X0_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELCONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELCONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)))),c_2Ellist_2ELCONS_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELDROP_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELDROP_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Ellist_2ELDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Ellist_2ELDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)))),c_2Ellist_2ELDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELDROP_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)))),c_2Ellist_2ELDROP_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),X0_2E0),s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),X0_2E0))),s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELFILTER_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELFILTER_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELFILTER_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Ellist_2ELFINITE_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),c_2Ellist_2ELFINITE_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELFLATTEN_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELFLATTEN_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELFLATTEN_2E1_2Emono_2EA_27d,axiom,
    ! [A_27d: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),tyop_2Ellist_2Ellist(A_27d)),c_2Ellist_2ELFLATTEN_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELGENLIST_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X1_2E0)))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELGENLIST_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELHD_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Ellist_2ELHD_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELHD_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELHD_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0)))) = j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ellist_2ELLENGTH_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELLENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0)))) = j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Ellist_2ELLENGTH_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELMAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELMAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELMAP_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELMAP_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELNTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELNTH_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) = s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ellist_2ELNTH_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ellist_2ELNTH_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ellist_2ELNTH_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELNTH_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(A_27c))),c_2Ellist_2ELNTH_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),c_2Ellist_2ELPREFIX_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELPREFIX_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool)),c_2Ellist_2ELPREFIX_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELREPEAT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELREPEAT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELTAKE_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27c),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)))),c_2Ellist_2ELTAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Ellist_2Ellist(A_27c),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELTL_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)))),c_2Ellist_2ELTL_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELTL__HD_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Ellist_2ELTL__HD_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELUNFOLD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0),s(A_27b,X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X0_2E0))),s(A_27b,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),X0_2E0))),s(A_27c,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0),s(A_27c,X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(A_27c,tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))),s(A_27c,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2ELUNFOLD_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELUNFOLD_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELUNZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E1(s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Ellist_2ELUNZIP_2E0),s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2ELZIP_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X0_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Ellist_2ELZIP_2E0),s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Earithmetic_2EMOD_2E2,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Earithmetic_2EMOD_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_2EMOD_2E0,X0_2E0),X1_2E0) ) ).

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

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

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2EA_27a_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__BIND_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Eoption_2EOPTION__BIND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2EOPTION__JOIN_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__JOIN_2E0),s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2Etyop_2Elist_2Elist_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27c_29_20mono_2Etyop_2Elist_2Elist_28A_27c_29,axiom,
    ! [A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,X1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(X0_2E0,X1_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,X0_2E0),X1_2E0) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27a_29_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),c_2Eoption_2EOPTION__MAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0))) ) ).

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

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

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27b),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(A_27c,A_27b),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Eoption_2ESOME_2E0),s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),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_2Elist_2ETAKE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Enum_2Enum,X1_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_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_2Elist_2ETAKE_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X0_2E0)))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),A_27a),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Elist_2Elist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))) = s(tyop_2Elist_2Elist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Ellist_2Ellist_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))) = s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2ETHE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(X0_2E0) = mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum,X0_2E0) ) ).

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

tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28A_27a_29_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27a_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Epair_2Eprod_28A_27a_2CA_27a_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27b_20mono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2EA_27c_20mono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27c_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2Ctyop_2Ellist_2Ellist_28A_27b_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),c_2Epair_2EUNCURRY_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),X0_2E0))) ) ).

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

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(arityeq1_2Ec_2Eset__relation_2Edomain_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Edomain_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),c_2Ellist_2Eevery_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2Eevery_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool)),c_2Ellist_2Eevery_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ellist_2Eexists_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),c_2Ellist_2Eexists_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Efinite__prefixes_2E2_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Efinite__prefixes_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2EfromList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2EfromList_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Elist_2EisPREFIX_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),c_2Elist_2EisPREFIX_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Elinear__order_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Eset__relation_2Elinear__order_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2Elinear__order__to__list__f_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ellist_2Elinear__order__to__list__f_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),c_2Ellist_2Elinear__order__to__list__f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2Ellength__rel_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Ellist_2Ellength__rel_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0)))),X1_2E0) ) ).

tff(arityeq1_2Ec_2Ellist_2Ellist__abs_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2Ellist__abs_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2Ellist__rep_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Ellist_2Ellist__rep_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Ellist_2Ellist__rep_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),c_2Ellist_2Ellist__rep_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(X1_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Ellist_2Elrep__ok_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ellist_2Elrep__ok_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Ebool),c_2Ellist_2Elrep__ok_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Eminimal__elements_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Eset__relation_2Eminimal__elements_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_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_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X0_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [A_27a: 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_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(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_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(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_2EA_27b_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28A_27b_2CA_27a_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Epair_2Eprod_28tyop_2Ellist_2Ellist_28A_27a_29_2CA_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(A_27a),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Elist_2Elist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Ellist_2Ellist_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Ellist_2Ellist_28A_27a_29_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0)),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(X0_2E0)))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2Etyop_2Ellist_2Ellist_28A_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X2_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),tyop_2Ellist_2Ellist(A_27b)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Ellist_2Ellist(A_27b),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Ebool,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(X1_2E0)))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),c_2Eoption_2Eoption__CASE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Ellist_2Ellist_28A_27b_29_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),X1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),tyop_2Ellist_2Ellist(A_27b))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,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_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Elist_2Elist_28A_27a_29_29_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),X1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),c_2Epair_2Epair__CASE_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Eset__relation_2Erange_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Eset__relation_2Erange_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Eset__relation_2Errestrict_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Eset__relation_2Errestrict_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),c_2Ellist_2EtoList_2E0),s(tyop_2Ellist_2Ellist(A_27a),X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ellist_2EtoList_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b))),c_2Ellist_2EtoList_2E0),s(tyop_2Ellist_2Ellist(A_27b),X0_2E0))) ) ).

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

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

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

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Ebool] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(V0_2E0)),s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29(V1_2E0)))) ) ).

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

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

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

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

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0,V1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),c_2Emin_2E_40_2E0) ).

tff(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29_29(mono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)))),c_2Ebool_2ECOND_2E0) ).

tff(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,axiom,
    ! [V0_2E0: mono_2Etyop_2Emin_2Ebool,V1_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V2_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0,V1_2E0,V2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V0_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V2_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ENONE_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Eoption_2Eoption(tyop_2Enum_2Enum))),c_2Eoption_2EOPTION__MAP_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2EOPTION__MAP_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_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(V0_2E0,V1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2EOPTION__MAP_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_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V1_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_29(mono_2Ec_2Eoption_2ESOME_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Enum_2Enum)),c_2Eoption_2ESOME_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Eoption_2ESOME_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0_2E0)))) ) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
    s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),i_mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ETHE_2E0_2Emono_2Etyop_2Enum_2Enum)) = s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),tyop_2Enum_2Enum),c_2Eoption_2ETHE_2E0) ).

tff(monoeq_2Emono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [V0_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(V0_2E0))) = s(tyop_2Enum_2Enum,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0_2E0)))) ) ).

tff(thm_2Ellist_2Elrep__ok__def,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V6x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V6x_2E0))
        <=> ( V6x_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0x_2E0)))))
        <=> ? [V1lrep__ok_27_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0x_2E0)))))
              & ! [V2a0_2E0: u] :
                  ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2a0_2E0)))))
                 => ( ! [V3x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
                    | ? [V4h_2E0: u,V5t_2E0: u] :
                        ( ! [V6x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6x_2E0)))) = s(tyop_2Eoption_2Eoption(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,V6x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V5t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V6x_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) )
                        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V1lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V5t_2E0))))) ) ) ) ) ) ) ).

tff(thm_2Ellist_2Ellist__TY__DEF,axiom,
    ! [A_27a: d] :
    ? [V0rep_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),c_2Ellist_2Elrep__ok_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),V0rep_2E0))))) ).

tff(thm_2Ellist_2Ellist__absrep,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0a_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),V0a_2E0) )
      & ! [V1r_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1r_2E0)))))
        <=> ( s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1r_2E0))))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1r_2E0) ) ) ) ).

tff(thm_2Ellist_2ELNIL,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
     => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F0_2E0))) ) ) ).

tff(thm_2Ellist_2ELCONS,axiom,
    ! [A_27a: d,F1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F0_2E0: u] :
      ( ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F1_2E0,V2n_2E0))
        <=> ( V2n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ( ! [V0h_2E0: u,V1t_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(A_27a,V0h_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Eoption_2Eoption(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(F1_2E0,V2n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) )
       => ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(A_27a,V0h_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELTL__HD__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0ll_2E0: u,V1h_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(A_27a,V1h_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2Ellist__rep_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_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,V1h_2E0))))) )
     => ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) ) ) ).

tff(thm_2Ellist_2ELHD,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ) ).

tff(thm_2Ellist_2ELTL,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0ll_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V2n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))) )
     => ( ! [V0ll_2E0: u,V1v_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(A_27a,V1v_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))))) )
       => ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELNTH,axiom,
    ! [A_27a: d] :
      ( ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELNTH_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__def,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0f_2E0: u,V3m_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V3m_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),V3m_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),c_2Ecombin_2EK_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0))))))) )
     => ( ! [V0f_2E0: u,V1z_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0))),s(A_27b,V1z_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)))),F1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0),s(A_27b,V1z_2E0))))))) )
       => ! [V0f_2E0: u,V1z_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0),s(A_27b,V1z_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2Ellist__abs_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V0f_2E0))),s(A_27b,V1z_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELTAKE,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3hd_2E0: u,V4tl_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(A_27a,V3hd_2E0))),s(tyop_2Elist_2Elist(A_27a),V4tl_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3hd_2E0),s(tyop_2Elist_2Elist(A_27a),V4tl_2E0))))) )
     => ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3hd_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3hd_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(A_27a,V3hd_2E0))))) )
       => ( ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
          & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))) ) ) ) ) ).

tff(thm_2Ellist_2ELMAP,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0f_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0) )
      & ! [V1f_2E0: u,V2h_2E0: u,V3t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V2h_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))) ) ) ).

tff(thm_2Ellist_2ELAPPEND,axiom,
    ! [A_27a: d] :
      ( ! [V0x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0) )
      & ! [V1h_2E0: u,V2t_2E0: u,V3x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V3x_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3x_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__def,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0)))))
    <=> ! [V1LFINITE_27_2E0: u] :
          ( ! [V2a0_2E0: u] :
              ( ( ( s(tyop_2Ellist_2Ellist(A_27a),V2a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
                | ? [V3h_2E0: u,V4t_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V2a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0))))) ) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2a0_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0))))) ) ) ).

tff(thm_2Ellist_2Ellength__rel__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1x_27_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_27_2E0))))))
    <=> ! [V2llength__rel_27_2E0: u] :
          ( ! [V3a0_2E0: u,V4a1_2E0: mono_2Etyop_2Enum_2Enum] :
              ( ( ( ( s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
                  & ( V4a1_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
                | ? [V5h_2E0: u,V6n_2E0: mono_2Etyop_2Enum_2Enum,V7t_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0))) )
                    & ( V4a1_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V6n_2E0) )
                    & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0)))),V6n_2E0)) ) )
             => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0)))),V4a1_2E0)) )
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V2llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0)))),V1x_27_2E0)) ) ) ).

tff(thm_2Ellist_2ELLENGTH,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0ll_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))),V1n_2E0) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))) )
     => ! [V0ll_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) ) ) ).

tff(thm_2Ellist_2EtoList,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Ellist_2EfromList__def,axiom,
    ! [A_27a: d] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V1t_2E0))))) ) ) ).

tff(thm_2Ellist_2ELDROP,axiom,
    ! [A_27a: d] :
      ( ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__JOIN_2E1(s(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELDROP_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))))) ) ) ).

tff(thm_2Ellist_2Eexists__def,axiom,
    ! [A_27a: d,V0x_2E0: u,V1x_27_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1x_27_2E0)))))
    <=> ! [V2exists_27_2E0: u] :
          ( ! [V3a0_2E0: u] :
              ( ( ? [V4h_2E0: u,V5t_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0x_2E0),s(A_27a,V4h_2E0))))) )
                | ? [V6h_2E0: u,V7t_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V6h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0))))) ) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V2exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1x_27_2E0))))) ) ) ).

tff(thm_2Ellist_2Eevery__def,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
    <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))) ) ).

tff(thm_2Ellist_2ELFILTER,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0P_2E0: u,V1ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
        <=> ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))) )
     => ! [V0P_2E0: u,V1ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))))))) ) ) ).

tff(thm_2Ellist_2ELFLATTEN,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0)))))
        <=> ( s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
     => ! [V0ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))))))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))))))))))))) ) ) ).

tff(thm_2Ellist_2ELZIP__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0l1_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0))))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELNIL_2E0) )
      & ! [V1l2_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1l2_2E0))))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELNIL_2E0) )
      & ! [V2h1_2E0: u,V3h2_2E0: u,V4t1_2E0: u,V5t2_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t1_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V3h2_2E0),s(tyop_2Ellist_2Ellist(A_27b),V5t2_2E0))))))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELCONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2h1_2E0),s(A_27b,V3h2_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),V4t1_2E0),s(tyop_2Ellist_2Ellist(A_27b),V5t2_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELUNZIP__THM,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0x_2E0: u,V1y_2E0: u,V3ll1_2E0: u,V4ll2_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))))),F0_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V3ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27b),V4ll2_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0x_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V1y_2E0),s(tyop_2Ellist_2Ellist(A_27b),V4ll2_2E0))))) )
     => ( ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E1(s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0))) )
        & ! [V0x_2E0: u,V1y_2E0: u,V2t_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E1(s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELCONS_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V0x_2E0),s(A_27b,V1y_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) = s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b))))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)))))),F0_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))))),s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E1(s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),V2t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__list__f__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1min_2E0: u] :
          ( p(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),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0)))))
        <=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0) ) )
     => ( ! [V0lo_2E0: u,V1min_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Eset__relation_2Errestrict_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EDIFF_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0))))),s(A_27a,c_2Epred__set_2ECHOICE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1min_2E0))))))))) )
       => ! [V0lo_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ellist_2Elinear__order__to__list__f_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)),c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Eminimal__elements_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Edomain_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Eset__relation_2Erange_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__def,axiom,
    ! [A_27a: d,F0_2E0: u,F2_2E0: u,F3_2E0: u,F1_2E0: u] :
      ( ! [V0l1_2E0: u,V1l2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0)))))
        <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0) ) )
     => ( ! [V2xs_2E0: u,V1l2_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0)))))
          <=> ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2xs_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2xs_2E0))) ) )
       => ( ! [V2xs_2E0: u,V3ys_2E0: u] : ( 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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs_2E0))),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V2xs_2E0),s(tyop_2Elist_2Elist(A_27a),V3ys_2E0)))) )
         => ( ! [V1l2_2E0: u,V2xs_2E0: u] : ( 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_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))),s(tyop_2Elist_2Elist(A_27a),V2xs_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F2_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Elist_2Elist(A_27a),V2xs_2E0)))))) )
           => ! [V0l1_2E0: u,V1l2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0)))))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__def,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V3lim_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3lim_2E0)))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V4n_2E0,V3lim_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V4n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)))))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ENONE_2E0))) )
     => ( ! [V0f_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V1n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))))))) )
       => ( ! [V0f_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) )
          & ! [V2f_2E0: u,V3lim_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V3lim_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3lim_2E0)))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) ) ) ) ) ).

tff(thm_2Ellist_2ELREPEAT__def,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0l_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2EMOD_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
     => ! [V0l_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))))) ) ) ).

tff(thm_2Ellist_2Elrep__ok__rules,axiom,
    ! [A_27a: d,F0_2E0: u,F2_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,F1_2E0: u] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
     => ( ! [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F2_2E0,V3n_2E0))
          <=> ( V3n_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
       => ( ! [V1h_2E0: u,V2t_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F1_2E0),s(A_27a,V1h_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)))) = s(tyop_2Eoption_2Eoption(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(F2_2E0,V3n_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V3n_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) )
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),F0_2E0)))))
            & ! [V1h_2E0: u,V2t_2E0: u] :
                ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2t_2E0)))))
               => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F1_2E0),s(A_27a,V1h_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V2t_2E0))))))) ) ) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__coind,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V5x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V5x_2E0))
        <=> ( V5x_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0lrep__ok_27_2E0: u] :
          ( ! [V1a0_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1a0_2E0)))))
             => ( ! [V2x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
                | ? [V3h_2E0: u,V4t_2E0: u] :
                    ( ! [V5x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V1a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5x_2E0)))) = s(tyop_2Eoption_2Eoption(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,V5x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V4t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V5x_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V4t_2E0))))) ) ) )
         => ! [V6a0_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Ebool),V0lrep__ok_27_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V6a0_2E0)))))
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V6a0_2E0))))) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__cases,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V4x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V4x_2E0))
        <=> ( V4x_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0a0_2E0)))))
        <=> ( ! [V1x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
            | ? [V2h_2E0: u,V3t_2E0: u] :
                ( ! [V4x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4x_2E0)))) = s(tyop_2Eoption_2Eoption(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,V4x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V3t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V4x_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) )
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V3t_2E0))))) ) ) ) ) ).

tff(thm_2Ellist_2Elrep__ok__alt,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0)))))
    <=> ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0)))))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))))))) ) ) ).

tff(thm_2Ellist_2Elrep__ok__MAP,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V1f_2E0: u,V0g_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V0g_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V0g_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))))) )
     => ! [V0g_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V0g_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27b)),V0g_2E0)))) ) ) ).

tff(thm_2Ellist_2Elrep__ok__FUNPOW__BIND,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0g_2E0: u,V3m_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V3m_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),V3m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))) )
     => ( ! [V0g_2E0: u,V1fz_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V1fz_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Eoption_2Eoption(A_27a),V1fz_2E0))) )
       => ! [V0g_2E0: u,V1fz_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Elrep__ok_2E1(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),V0g_2E0))),s(tyop_2Eoption_2Eoption(A_27a),V1fz_2E0))))))) ) ) ).

tff(thm_2Ellist_2Ellist__rep__LCONS,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V2x_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V2x_2E0))
        <=> ( V2x_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
     => ! [V0t_2E0: u,V1h_2E0: u,V2x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2x_2E0)))) = s(tyop_2Eoption_2Eoption(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,V2x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1h_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V2x_2E0,mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))))) ) ) ).

tff(thm_2Ellist_2Ellist__rep__LNIL,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0x_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ).

tff(thm_2Ellist_2ELTL__HD__LNIL,axiom,
    ! [A_27a: d] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ENONE_2E0) ) ).

tff(thm_2Ellist_2ELTL__HD__LCONS,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0),s(A_27a,V1h_2E0))))) ) ).

tff(thm_2Ellist_2ELTL__HD__HD,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) ) ).

tff(thm_2Ellist_2ELTL__HD__TL,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Epair_2EFST_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) ) ).

tff(thm_2Ellist_2ELHD__LCONS,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1h_2E0))) ) ).

tff(thm_2Ellist_2ELTL__LCONS,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))) ) ).

tff(thm_2Ellist_2ELHDTL__CONS__THM,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0h_2E0))) )
      & ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) ) ) ).

tff(thm_2Ellist_2Ellist__CASES,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      | ? [V1h_2E0: u,V2t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) ) ) ).

tff(thm_2Ellist_2ELTL__HD__11,axiom,
    ! [A_27a: d,V0ll2_2E0: u,V1ll1_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll2_2E0))) )
     => ( s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V0ll2_2E0) ) ) ).

tff(thm_2Ellist_2ELHD__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0h_2E0))) ) ) ).

tff(thm_2Ellist_2ELTL__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0) )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))) ) ) ).

tff(thm_2Ellist_2ELCONS__NOT__NIL,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) != s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) != s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) ) ) ).

tff(thm_2Ellist_2ELCONS__11,axiom,
    ! [A_27a: d,V0h1_2E0: u,V1t1_2E0: u,V2h2_2E0: u,V3t2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t1_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t2_2E0))) )
    <=> ( ( s(A_27a,V0h1_2E0) = s(A_27a,V2h2_2E0) )
        & ( s(tyop_2Ellist_2Ellist(A_27a),V1t1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V3t2_2E0) ) ) ) ).

tff(thm_2Ellist_2ELTL__HD__iff,axiom,
    ! [A_27a: d,V0x_2E0: u,V1t_2E0: u,V2h_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0),s(A_27a,V2h_2E0))))) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) ) )
      & ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ENONE_2E0) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELHD__EQ__NONE,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
      & ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELTL__EQ__NONE,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
      & ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) )
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELHDTL__EQ__SOME,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u,V2ll_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) )
    <=> ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V0h_2E0))) )
        & ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) ) ) ) ).

tff(thm_2Ellist_2ELNTH__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
      & ! [V1h_2E0: u,V2t_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V2t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V1h_2E0))) )
      & ! [V3n_2E0: mono_2Etyop_2Enum_2Enum,V4h_2E0: u,V5t_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27c),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V3n_2E0))),s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27c),V5t_2E0))))) = s(tyop_2Eoption_2Eoption(A_27c),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Ellist_2Ellist(A_27c),V5t_2E0))) ) ) ).

tff(thm_2Ellist_2ELNTH__rep,axiom,
    ! [A_27a: d,V0i_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2Ellist__rep_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0i_2E0)))) ) ).

tff(thm_2Ellist_2ELNTH__EQ,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0) )
    <=> ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))) ) ) ).

tff(thm_2Ellist_2ELUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0f_2E0: u,V3v1_2E0: u,V4v2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))),s(A_27a,V3v1_2E0))),s(A_27b,V4v2_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V4v2_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V3v1_2E0))))) )
     => ( ! [V0f_2E0: u,V2v_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V2v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))))) )
       => ! [V0f_2E0: u,V1x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__UNIQUE,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1g_2E0: u,V4v1_2E0: u,V5v2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(A_27a,V4v1_2E0))),s(A_27b,V5v2_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V5v2_2E0),s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V4v1_2E0))))) )
     => ( ! [V1g_2E0: u,V3v_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) )
       => ! [V0f_2E0: u,V1g_2E0: u] :
            ( ! [V2x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) )
           => ! [V6y_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V6y_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V6y_2E0))) ) ) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__LTL__HD,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),c_2Ellist_2ELTL__HD_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) ) ).

tff(thm_2Ellist_2ELTL__HD__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Epair_2E_23_23_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) ) ).

tff(thm_2Ellist_2ELNTH__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(A_27b,V4tx_2E0))),s(A_27a,V5hx_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V4tx_2E0))))) )
     => ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))))) )
       => ! [V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))))) )
            & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))))) ) ) ) ) ).

tff(thm_2Ellist_2ELNTH__LUNFOLD__compute,axiom,
    ! [A_27a: d,A_27b: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V2n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F3_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(A_27b,V4tx_2E0))),s(A_27a,V5hx_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V2n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V4tx_2E0))))) )
     => ( ! [V2n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F3_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))))) )
       => ( ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V8tx_2E0: u,V9hx_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(A_27b,V8tx_2E0))),s(A_27a,V9hx_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V6n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V8tx_2E0))))) )
         => ( ! [V6n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V7v_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),V7v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V7v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))),F2_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))))) )
           => ! [V0x_2E0: u,V1f_2E0: u] :
                ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) )
                & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V2n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))))) )
                & ! [V6n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V6n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(A_27a)))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V6n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))))) ) ) ) ) ) ) ).

tff(thm_2Ellist_2ELHD__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) ) ).

tff(thm_2Ellist_2ELTL__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Ellist_2Ellist(A_27a)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELUNFOLD_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V1f_2E0),s(A_27b,V0x_2E0))))) ) ).

tff(thm_2Ellist_2Ellist__Axiom__1,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1g_2E0: u,V4a_2E0: u,V5b_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V5b_2E0),s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V4a_2E0))))) )
     => ( ! [V1g_2E0: u,V3v_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) )
       => ! [V0f_2E0: u] :
          ? [V1g_2E0: u] :
          ! [V2x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) ) ) ) ).

tff(thm_2Ellist_2Ellist__Axiom__1ue,axiom,
    ! [A_27a: d,A_27b: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V1g_2E0: u,V4a_2E0: u,V5b_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(A_27a,V4a_2E0))),s(A_27b,V5b_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V5b_2E0),s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V4a_2E0))))) )
     => ( ! [V1g_2E0: u,V3v_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Ellist_2Ellist(A_27b)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) )
       => ( ! [V0f_2E0: u,V1g_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0)))))
            <=> ! [V2x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0))))) ) )
         => ! [V0f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))))))) ) ) ) ).

tff(thm_2Ellist_2Ellist__ue__Axiom,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u] :
      ( ! [V0f_2E0: u,V1g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0)))))
        <=> ( ! [V2x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2x_2E0))))) )
            & ! [V3x_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V3x_2E0))))) ) ) )
     => ! [V0f_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0))))))) ) ).

tff(thm_2Ellist_2Ellist__Axiom,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u] :
    ? [V1g_2E0: u] :
      ( ! [V2x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2x_2E0))))) )
      & ! [V3x_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V3x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Ellist_2Ellist(A_27b)),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V3x_2E0))))) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__BISIMULATION,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f1_2E0: u,V1f2_2E0: u,V2x1_2E0: u,V3x2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f1_2E0),s(A_27a,V2x1_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1f2_2E0),s(A_27c,V3x2_2E0))) )
    <=> ? [V4R_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V2x1_2E0))),s(A_27c,V3x2_2E0)))))
          & ! [V5y1_2E0: u,V6y2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V5y1_2E0))),s(A_27c,V6y2_2E0)))))
             => ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f1_2E0),s(A_27a,V5y1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ENONE_2E0) )
                  & ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1f2_2E0),s(A_27c,V6y2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2ENONE_2E0) ) )
                | ? [V7h_2E0: u,V8t1_2E0: u,V9t2_2E0: u] :
                    ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f1_2E0),s(A_27a,V5y1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V8t1_2E0),s(A_27b,V7h_2E0))))) )
                    & ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),V1f2_2E0),s(A_27c,V6y2_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,V9t2_2E0),s(A_27b,V7h_2E0))))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V8t1_2E0))),s(A_27c,V9t2_2E0))))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__BISIMULATION0,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0) )
    <=> ? [V2R_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))
          & ! [V3ll3_2E0: u,V4ll4_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0)))))
             => ( ( ( s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
                  & ( s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
                | ? [V5h_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6t1_2E0))) )
                    & ( s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t2_2E0))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6t1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V7t2_2E0))))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__BISIMULATION,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0) )
    <=> ? [V2R_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))
          & ! [V3ll3_2E0: u,V4ll4_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0)))))
             => ( ( ( s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
                  & ( s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
                | ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0))) )
                  & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0))))))))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELLIST__STRONG__BISIMULATION,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0) )
    <=> ? [V2R_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))
          & ! [V3ll3_2E0: u,V4ll4_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0)))))
             => ( ( s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0) )
                | ? [V5h_2E0: u,V6t1_2E0: u,V7t2_2E0: u] :
                    ( ( s(tyop_2Ellist_2Ellist(A_27a),V3ll3_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6t1_2E0))) )
                    & ( s(tyop_2Ellist_2Ellist(A_27a),V4ll4_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V5h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t2_2E0))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),V2R_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6t1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V7t2_2E0))))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V4tx_2E0: u,V5hx_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(A_27b,V4tx_2E0))),s(A_27a,V5hx_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E1(s(A_27a,V5hx_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V4tx_2E0))))))) )
     => ( ! [V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u,V3v_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))))),F1_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))))) )
       => ! [V0x_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2f_2E0: u] :
            ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
            & ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))))) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Eoption_2ENONE_2E0) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3h_2E0: u,V4t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))),s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27c),tyop_2Elist_2Elist(A_27c)),c_2Elist_2ECONS_2E1(s(A_27c,V3h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27c)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))))) ) ) ).

tff(thm_2Ellist_2ELTAKE__SNOC__LNTH,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V2l_2E0: u,V3e_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))),s(A_27a,V3e_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),V2l_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V3e_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))))))) )
     => ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V2l_2E0))))) )
       => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__EQ__NONE__LNTH,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__NIL__EQ__SOME,axiom,
    ! [A_27a: d,V0l_2E0: u,V1m_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) )
    <=> ( ( V1m_2E0 = mono_2Ec_2Enum_2E0_2E0 )
        & ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__NIL__EQ__NONE,axiom,
    ! [A_27a: d,V0m_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) )
    <=> p(mono_2Ec_2Eprim__rec_2E_3C_2E2(mono_2Ec_2Enum_2E0_2E0,V0m_2E0)) ) ).

tff(thm_2Ellist_2ELTAKE__EQ,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0) )
    <=> ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))) ) ) ).

tff(thm_2Ellist_2ELTAKE__CONS__EQ__NONE,axiom,
    ! [A_27a: d,V0m_2E0: mono_2Etyop_2Enum_2Enum,V1h_2E0: u,V2t_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) )
    <=> ? [V3n_2E0: mono_2Etyop_2Enum_2Enum] :
          ( ( V0m_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V3n_2E0) )
          & ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__CONS__EQ__SOME,axiom,
    ! [A_27a: d,V0m_2E0: mono_2Etyop_2Enum_2Enum,V1h_2E0: u,V2t_2E0: u,V3l_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) )
    <=> ( ( ( V0m_2E0 = mono_2Ec_2Enum_2E0_2E0 )
          & ( s(tyop_2Elist_2Elist(A_27a),V3l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
        | ? [V4n_2E0: mono_2Etyop_2Enum_2Enum,V5l_27_2E0: u] :
            ( ( V0m_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V4n_2E0) )
            & ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V5l_27_2E0))) )
            & ( s(tyop_2Elist_2Elist(A_27a),V3l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ECONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Elist_2Elist(A_27a),V5l_27_2E0))) ) ) ) ) ).

tff(thm_2Ellist_2ELTAKE__EQ__SOME__CONS,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2x_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2x_2E0))) )
     => ! [V3h_2E0: u] :
        ? [V4y_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V4y_2E0))) ) ) ).

tff(thm_2Ellist_2ELMAP__APPEND,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1ll1_2E0: u,V2ll2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0))))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0))))) ) ).

tff(thm_2Ellist_2ELAPPEND__EQ__LNIL,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
    <=> ( ( s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
        & ( s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELAPPEND__ASSOC,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u,V2ll3_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2ll3_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll3_2E0))))) ) ).

tff(thm_2Ellist_2ELMAP__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0),s(tyop_2Ellist_2Ellist(A_27c),V2ll_2E0))))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V1g_2E0))),s(tyop_2Ellist_2Ellist(A_27c),V2ll_2E0))) ) ).

tff(thm_2Ellist_2ELAPPEND__NIL__2ND,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) ) ).

tff(thm_2Ellist_2ELHD__LAPPEND,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1l1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0)))))
        <=> ( s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
     => ! [V0l2_2E0: u,V1l1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))))) ) ) ).

tff(thm_2Ellist_2ELTL__LAPPEND,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1l1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0)))))
        <=> ( s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
     => ! [V0l2_2E0: u,V1l1_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))))),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELTAKE__LAPPEND1,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l1_2E0: u,V2l2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0)))))))
     => ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))) ) ) ).

tff(thm_2Ellist_2ELFINITE__rules,axiom,
    ! [A_27a: d] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
      & ! [V0h_2E0: u,V1t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__ind,axiom,
    ! [A_27a: d,V0LFINITE_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
        & ! [V1h_2E0: u,V2t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))))) ) )
     => ! [V3a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__strongind,axiom,
    ! [A_27a: d,V0LFINITE_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
        & ! [V1h_2E0: u,V2t_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))))) ) )
     => ! [V3a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0)))))
    <=> ( ( s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
        | ? [V1h_2E0: u,V2t_2E0: u] :
            ( ( s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0)))) ) ) ).

tff(thm_2Ellist_2ELFINITE,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
    <=> ? [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2Ellength__rel__rules,axiom,
    ! [A_27a: d] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0))))))
      & ! [V0h_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0))))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))))))) ) ) ).

tff(thm_2Ellist_2Ellength__rel__ind,axiom,
    ! [A_27a: d,V0llength__rel_27_2E0: u] :
      ( ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))),mono_2Ec_2Enum_2E0_2E0))
        & ! [V1h_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3t_2E0: u] :
            ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))),V2n_2E0))
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))) ) )
     => ! [V4a0_2E0: u,V5a1_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V4a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5a1_2E0))))))
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4a0_2E0)))),V5a1_2E0)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__strongind,axiom,
    ! [A_27a: d,V0llength__rel_27_2E0: u] :
      ( ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))),mono_2Ec_2Enum_2E0_2E0))
        & ! [V1h_2E0: u,V2n_2E0: mono_2Etyop_2Enum_2Enum,V3t_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0))))))
              & p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))),V2n_2E0)) )
           => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))))),mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))) ) )
     => ! [V4a0_2E0: u,V5a1_2E0: mono_2Etyop_2Enum_2Enum] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V4a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V5a1_2E0))))))
         => p(mono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),V0llength__rel_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4a0_2E0)))),V5a1_2E0)) ) ) ).

tff(thm_2Ellist_2Ellength__rel__cases,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: mono_2Etyop_2Enum_2Enum] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1a1_2E0))))))
    <=> ( ( ( s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
          & ( V1a1_2E0 = mono_2Ec_2Enum_2E0_2E0 ) )
        | ? [V2h_2E0: u,V3n_2E0: mono_2Etyop_2Enum_2Enum,V4t_2E0: u] :
            ( ( s(tyop_2Ellist_2Ellist(A_27a),V0a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0))) )
            & ( V1a1_2E0 = mono_2Ec_2Enum_2ESUC_2E1(V3n_2E0) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Ellength__rel_2E2(s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n_2E0)))))) ) ) ) ).

tff(thm_2Ellist_2ELLENGTH__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0)))))) = mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E0,j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))))) ) ) ).

tff(thm_2Ellist_2ELLENGTH__0,axiom,
    ! [A_27a: d,V0x_2E0: u] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) )
    <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0x_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__HAS__LENGTH,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ? [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1n_2E0) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__NO__LENGTH,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) = mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum ) ) ).

tff(thm_2Ellist_2ELFINITE__LLENGTH,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
    <=> ? [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1n_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__INDUCTION,axiom,
    ! [A_27a: d,V0LFINITE_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
        & ! [V1h_2E0: u,V2t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))))) ) )
     => ! [V3a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__STRONG__INDUCTION,axiom,
    ! [A_27a: d,V0LFINITE_27_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
        & ! [V1h_2E0: u,V2t_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))))) ) )
     => ! [V3a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V0LFINITE_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3a0_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFINITE__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1ll_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))) ) ).

tff(thm_2Ellist_2ELFINITE__APPEND,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))))
    <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))))) ) ) ).

tff(thm_2Ellist_2ELTAKE__LNTH__EL,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2m_2E0: mono_2Etyop_2Enum_2Enum,V3l_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) )
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V2m_2E0,V0n_2E0)) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2m_2E0)),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__APPEND,axiom,
    ! [A_27a: d,V0ll1_2E0: u,V1ll2_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0)))))
     => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0) ) ) ).

tff(thm_2Ellist_2ELFINITE__LAPPEND__IMP__NIL,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ! [V1l2_2E0: u] :
          ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) )
         => ( s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELLENGTH__MAP,axiom,
    ! [A_27a: d,A_27b: d,V0ll_2E0: u,V1f_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))) = j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) ) ).

tff(thm_2Ellist_2ELLENGTH__APPEND,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0ll1_2E0: u,V1ll2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))))) ) )
     => ! [V0ll1_2E0: u,V1ll2_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0)))),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll1_2E0))))),mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll2_2E0))))))),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) ) ) ).

tff(thm_2Ellist_2EtoList__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) )
      & ! [V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V0h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E1(s(A_27b,V0h_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27b)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27b),V1t_2E0))))) ) ) ).

tff(thm_2Ellist_2EfromList__EQ__LNIL,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
    <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) ) ).

tff(thm_2Ellist_2ELHD__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EHD_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ).

tff(thm_2Ellist_2ELTL__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))))) ) ).

tff(thm_2Ellist_2ELFINITE__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ).

tff(thm_2Ellist_2ELLENGTH__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ).

tff(thm_2Ellist_2ELTAKE__fromList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ).

tff(thm_2Ellist_2Efrom__toList,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) ).

tff(thm_2Ellist_2ELFINITE__toList,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ? [V1l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))) ) ) ).

tff(thm_2Ellist_2ELFINITE__toList__SOME,axiom,
    ! [A_27a: d,V0ll_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2EIS__SOME_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))) ) ).

tff(thm_2Ellist_2Eto__fromList,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))))) = s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__LAPPEND2,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l1_2E0: u,V2l2_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) )
     => ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0)))))))),s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0))))) ) ) ).

tff(thm_2Ellist_2ELNTH__fromList,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Ellist_2Elnth__fromList__some,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u] :
      ( p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))))
    <=> ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Elist_2Elist(A_27a),V1l_2E0))))) ) ) ).

tff(thm_2Ellist_2ELDROP__FUNPOW,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V2m_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),V2m_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),V2m_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E0))) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Earithmetic_2EFUNPOW_2E3(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))) ) ) ).

tff(thm_2Ellist_2ELDROP__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d] :
      ( ! [V0ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2ENONE_2E0) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3h_2E0: u,V4t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V2n_2E0))),s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELCONS_2E2(s(A_27c,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27c),V4t_2E0))) ) ) ).

tff(thm_2Ellist_2ELDROP1__THM,axiom,
    ! [A_27a: d] : ( s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELDROP_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))))) = s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E0) ) ).

tff(thm_2Ellist_2ELNTH__HD__LDROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELHD_2E0))) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__TAKE,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
        ? [V2y_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2y_2E0))) ) ) ).

tff(thm_2Ellist_2ELFINITE__TAKE,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))) )
     => ? [V2y_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2y_2E0))) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__DROP,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
     => ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
        ? [V2y_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2y_2E0))) ) ) ).

tff(thm_2Ellist_2ELFINITE__DROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))) )
     => ? [V2y_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2y_2E0))) ) ) ).

tff(thm_2Ellist_2ELTAKE__DROP,axiom,
    ! [A_27a: d] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
          ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
         => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))))) = s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0) ) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3ll_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0)))))
            & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V2n_2E0,mono_2Ec_2Eoption_2ETHE_2E1_2Emono_2Etyop_2Enum_2Enum(j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0))))))) )
         => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0))))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0))))))) = s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0) ) ) ) ).

tff(thm_2Ellist_2ELDROP__ADD,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V1k2_2E0: mono_2Etyop_2Enum_2Enum,V3ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k2_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k2_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V3ll_2E0))) )
     => ! [V0k1_2E0: mono_2Etyop_2Enum_2Enum,V1k2_2E0: mono_2Etyop_2Enum_2Enum,V2x_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V0k1_2E0,V1k2_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0k1_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2x_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1k2_2E0)))))) ) ) ).

tff(thm_2Ellist_2ELDROP__SOME__LLENGTH,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1m_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3l_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0))) )
        & ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1m_2E0) ) )
     => ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0n_2E0,V1m_2E0))
        & ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V1m_2E0,V0n_2E0)) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__LNTH__NONE,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
    <=> ? [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2Einfinite__lnth__some,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
    <=> ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] :
        ? [V2x_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))) ) ) ).

tff(thm_2Ellist_2ELNTH__LAPPEND,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V2l1_2E0: u,V1l2_2E0: u,V3m_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3m_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,V3m_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(V0n_2E0,V3m_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l2_2E0: u,V2l1_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) ) ) ).

tff(thm_2Ellist_2ELNTH__ADD,axiom,
    ! [A_27a: d,V0a_2E0: mono_2Etyop_2Enum_2Enum,V1b_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2B_2E2(V0a_2E0,V1b_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0a_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Ellist_2ELNTH_2E1(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1b_2E0)))))) ) ).

tff(thm_2Ellist_2Elnth__some__down__closed,axiom,
    ! [A_27a: d,V0ll_2E0: u,V1x_2E0: u,V2n1_2E0: mono_2Etyop_2Enum_2Enum,V3n2_2E0: mono_2Etyop_2Enum_2Enum] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n1_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V1x_2E0))) )
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V3n2_2E0,V2n1_2E0)) )
     => ? [V4y_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3n2_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V4y_2E0))) ) ) ).

tff(thm_2Ellist_2Eexists__rules,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1h_2E0: u,V2t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1h_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))))) )
      & ! [V3h_2E0: u,V4t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0))))))) ) ) ).

tff(thm_2Ellist_2Eexists__ind,axiom,
    ! [A_27a: d,V0P_2E0: u,V1exists_27_2E0: u] :
      ( ( ! [V2h_2E0: u,V3t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))))) )
        & ! [V4h_2E0: u,V5t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))))) ) )
     => ! [V6a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0))))) ) ) ).

tff(thm_2Ellist_2Eexists__strongind,axiom,
    ! [A_27a: d,V0P_2E0: u,V1exists_27_2E0: u] :
      ( ( ! [V2h_2E0: u,V3t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))))) )
        & ! [V4h_2E0: u,V5t_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))))) ) )
     => ! [V6a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1exists_27_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0))))) ) ) ).

tff(thm_2Ellist_2Eexists__cases,axiom,
    ! [A_27a: d,V0P_2E0: u,V1a0_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1a0_2E0)))))
    <=> ( ? [V2h_2E0: u,V3t_2E0: u] :
            ( ( s(tyop_2Ellist_2Ellist(A_27a),V1a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0))))) )
        | ? [V4h_2E0: u,V5t_2E0: u] :
            ( ( s(tyop_2Ellist_2Ellist(A_27a),V1a0_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))) )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2Eexists__thm,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))) = mono_2Ec_2Ebool_2EF_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1h_2E0)))))
          | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2Eexists__LNTH,axiom,
    ! [A_27a: d,V0P_2E0: u,V1l_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0)))))
    <=> ? [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3e_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3e_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3e_2E0))))) ) ) ).

tff(thm_2Ellist_2EMONO__exists,axiom,
    ! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Ellist_2Eexists__strong__ind,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ( ! [V2h_2E0: u,V3t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))))) )
        & ! [V4h_2E0: u,V5t_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))))) ) )
     => ! [V6a0_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6a0_2E0))))) ) ) ).

tff(thm_2Ellist_2Eexists__LDROP,axiom,
    ! [A_27a: d,V0ll_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eexists_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
    <=> ? [V2n_2E0: mono_2Etyop_2Enum_2Enum,V3a_2E0: u,V4t_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V2n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V3a_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4t_2E0))))) )
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3a_2E0))))) ) ) ).

tff(thm_2Ellist_2Eevery__coind,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ! [V2h_2E0: u,V3t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0))))) ) )
     => ! [V4ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4ll_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V4ll_2E0))))) ) ) ).

tff(thm_2Ellist_2Eevery__thm,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1h_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELL__ALL__THM,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2P_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))) = mono_2Ec_2Ebool_2ET_2E0 )
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0)))))))
      <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V1h_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))))) ) ) ) ).

tff(thm_2Ellist_2EMONO__every,axiom,
    ! [A_27a: d,V0l_2E0: u,V1Q_2E0: u,V2P_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))))) ) ) ).

tff(thm_2Ellist_2Eevery__strong__coind,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ( ! [V2h_2E0: u,V3t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3t_2E0)))))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2h_2E0))))) )
        & ! [V4h_2E0: u,V5t_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0)))))))
           => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0)))))
              | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V5t_2E0))))) ) ) )
     => ! [V6ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),V1Q_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6ll_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V6ll_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFILTER__THM,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0P_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ! [V1P_2E0: u,V2h_2E0: u,V3t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V3t_2E0))))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(A_27b,V2h_2E0))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Ellist_2Ellist(A_27b),V3t_2E0))))),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Ellist_2Ellist(A_27b),V3t_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFILTER__NIL,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
     => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ).

tff(thm_2Ellist_2ELFILTER__EQ__NIL,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ll_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ebool_2E_7E_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))))) ) ).

tff(thm_2Ellist_2ELFILTER__APPEND,axiom,
    ! [A_27a: d,V0P_2E0: u,V1ll1_2E0: u,V2ll2_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0)))))
     => ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFILTER_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll2_2E0))))) ) ) ).

tff(thm_2Ellist_2ELFLATTEN__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0t_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELNIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ! [V1tl_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),V0t_2E0))))) = s(tyop_2Ellist_2Ellist(A_27c),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27c)),V0t_2E0))) )
      & ! [V2h_2E0: u,V3t_2E0: u,V4tl_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELCONS_2E2(s(A_27d,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27d),V3t_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),V4tl_2E0))))) = s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELCONS_2E2(s(A_27d,V2h_2E0),s(tyop_2Ellist_2Ellist(A_27d),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27d),V3t_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27d)),V4tl_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELFLATTEN__APPEND,axiom,
    ! [A_27a: d,V0h_2E0: u,V1t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0h_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V1t_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0h_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V1t_2E0))))) ) ).

tff(thm_2Ellist_2ELFLATTEN__EQ__NIL,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
    <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2Eevery_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),V0ll_2E0))))) ) ).

tff(thm_2Ellist_2ELFLATTEN__SINGLETON,axiom,
    ! [A_27a: d,V0h_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELFLATTEN_2E1(s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELCONS_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0h_2E0),s(tyop_2Ellist_2Ellist(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELNIL_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),V0h_2E0) ) ).

tff(thm_2Ellist_2ELZIP__LUNZIP,axiom,
    ! [A_27a: d,A_27b: d,V0ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Ellist_2ELZIP_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELUNZIP_2E1(s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ll_2E0))))) = s(tyop_2Ellist_2Ellist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ll_2E0) ) ).

tff(thm_2Ellist_2ELUNFOLD__THM,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1x_2E0: u,V2v1_2E0: u,V3v2_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ENONE_2E0) )
       => ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0) ) )
      & ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2v1_2E0),s(A_27b,V3v2_2E0))))) )
       => ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V3v2_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V0f_2E0),s(A_27a,V2v1_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELLIST__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( ( ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V0f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0) )
            & ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0) ) )
          | ? [V3h_2E0: u,V4y_2E0: u] :
              ( ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V0f_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V0f_2E0),s(A_27a,V4y_2E0))))) )
              & ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V2x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V3h_2E0),s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V4y_2E0))))) ) ) )
     => ! [V5x_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V0f_2E0),s(A_27a,V5x_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Ellist_2Ellist(A_27b)),V1g_2E0),s(A_27a,V5x_2E0))) ) ) ).

tff(thm_2Ellist_2ELUNFOLD__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1f_2E0: u,V2s_2E0: u,V3ll_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2s_2E0))),s(tyop_2Ellist_2Ellist(A_27b),V3ll_2E0)))))
        & ! [V4s_2E0: u,V5ll_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4s_2E0))),s(tyop_2Ellist_2Ellist(A_27b),V5ll_2E0)))))
           => ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1f_2E0),s(A_27a,V4s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ENONE_2E0) )
                & ( s(tyop_2Ellist_2Ellist(A_27b),V5ll_2E0) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELNIL_2E0) ) )
              | ? [V6s_27_2E0: u,V7x_2E0: u,V8ll_27_2E0: u] :
                  ( ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1f_2E0),s(A_27a,V4s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V6s_27_2E0),s(A_27b,V7x_2E0))))) )
                  & ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27b),V5ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V7x_2E0))) )
                  & ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27b),V5ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27b)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27b),V8ll_27_2E0))) )
                  & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27b),tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6s_27_2E0))),s(tyop_2Ellist_2Ellist(A_27b),V8ll_27_2E0))))) ) ) ) )
     => ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27a,A_27b))),V1f_2E0),s(A_27a,V2s_2E0))) = s(tyop_2Ellist_2Ellist(A_27b),V3ll_2E0) ) ) ).

tff(thm_2Ellist_2ELMAP__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V0f_2E0: u,V4x_2E0: u,V5y_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(A_27c,V4x_2E0))),s(A_27a,V5y_2E0))) = s(tyop_2Epair_2Eprod(A_27c,A_27b),c_2Epair_2E_2C_2E2(s(A_27c,V4x_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V5y_2E0))))) )
     => ( ! [V0f_2E0: u,V1g_2E0: u,V3s_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1g_2E0))),s(A_27c,V3s_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27c,A_27a),tyop_2Epair_2Eprod(A_27c,A_27b)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27c,A_27b)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1g_2E0),s(A_27c,V3s_2E0))))) )
       => ! [V0f_2E0: u,V1g_2E0: u,V2s_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1g_2E0),s(A_27c,V2s_2E0))))) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(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,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27b))))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27c,A_27a))),V1g_2E0))),s(A_27c,V2s_2E0))) ) ) ) ).

tff(thm_2Ellist_2ELNTH__LDROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2x_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2x_2E0))) ) ) ).

tff(thm_2Ellist_2ELAPPEND__fromList,axiom,
    ! [A_27a: d,V0l1_2E0: u,V1l2_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V1l2_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(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))))) ) ).

tff(thm_2Ellist_2ELTAKE__LENGTH,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) )
     => ( V0n_2E0 = j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0)))) ) ) ).

tff(thm_2Ellist_2ELTAKE__TAKE__LESS,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1m_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u,V3l_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V3l_2E0))) )
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V1m_2E0,V0n_2E0)) )
     => ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ETAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Elist_2Elist(A_27a),V3l_2E0))))) ) ) ).

tff(thm_2Ellist_2ELTAKE__LLENGTH__NONE,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1m_2E0: mono_2Etyop_2Enum_2Enum,V2ll_2E0: u] :
      ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0n_2E0) )
        & p(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,V1m_2E0)) )
     => ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2ELTAKE__LLENGTH__SOME,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
      ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0n_2E0) )
     => ? [V2l_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) )
          & ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2l_2E0))) ) ) ) ).

tff(thm_2Ellist_2EtoList__LAPPEND__APPEND,axiom,
    ! [A_27a: d,V0x_2E0: u,V1l2_2E0: u,V2l1_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V0x_2E0))) )
     => ( s(tyop_2Elist_2Elist(A_27a),V0x_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EAPPEND_2E2(s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))))),s(tyop_2Elist_2Elist(A_27a),c_2Eoption_2ETHE_2E1(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELNTH__LLENGTH__NONE,axiom,
    ! [A_27a: d,V0x_2E0: mono_2Etyop_2Enum_2Enum,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] :
      ( ( ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0x_2E0) )
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0x_2E0,V1n_2E0)) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2ELNTH__NONE__MONO,axiom,
    ! [A_27a: d,V0m_2E0: mono_2Etyop_2Enum_2Enum,V1n_2E0: mono_2Etyop_2Enum_2Enum,V2l_2E0: u] :
      ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0m_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) )
        & p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V0m_2E0,V1n_2E0)) )
     => ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__llist__eq,axiom,
    ! [A_27a: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V2ll_2E0: u,V3x_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(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0)))))
        <=> ? [V4i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) ) )
     => ( ! [V2ll_2E0: u,V3x_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0))))) )
       => ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))))
            <=> ? [V7i_2E0: mono_2Etyop_2Enum_2Enum,V8j_2E0: mono_2Etyop_2Enum_2Enum] :
                  ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V7i_2E0,V8j_2E0))
                  & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0))) )
                  & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8j_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6y_2E0))) ) ) )
         => ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27a,V6y_2E0))),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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))))) )
           => ! [V0lo_2E0: u,V1X_2E0: u] :
                ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))
                  & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))) )
               => ? [V2ll_2E0: u] :
                    ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))) )
                    & ( s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))))) )
                    & ! [V9i_2E0: mono_2Etyop_2Enum_2Enum,V10j_2E0: mono_2Etyop_2Enum_2Enum,V11x_2E0: u] :
                        ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V11x_2E0))) )
                          & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V10j_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V11x_2E0))) ) )
                       => ( V9i_2E0 = V10j_2E0 ) ) ) ) ) ) ) ) ).

tff(thm_2Ellist_2Elinear__order__to__llist,axiom,
    ! [A_27a: d,F3_2E0: u,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V2ll_2E0: u,V3x_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(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0)))))
        <=> ? [V4i_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V4i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V3x_2E0))) ) )
     => ( ! [V2ll_2E0: u,V3x_2E0: u] : ( s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F3_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V3x_2E0))))) )
       => ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0)))))
            <=> ? [V7i_2E0: mono_2Etyop_2Enum_2Enum,V8j_2E0: mono_2Etyop_2Enum_2Enum] :
                  ( p(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V7i_2E0,V8j_2E0))
                  & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V7i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V5x_2E0))) )
                  & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V8j_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V6y_2E0))) ) ) )
         => ( ! [V2ll_2E0: u,V5x_2E0: u,V6y_2E0: u] : ( s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27a),c_2Epair_2E_2C_2E2(s(A_27a,V5x_2E0),s(A_27a,V6y_2E0))),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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))),s(A_27a,V5x_2E0))),s(A_27a,V6y_2E0))))) )
           => ! [V0lo_2E0: u,V1X_2E0: u] :
                ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Elinear__order_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0)))))
                  & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eset__relation_2Efinite__prefixes_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0))))) )
               => ? [V2ll_2E0: u] :
                    ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1X_2E0) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))))) )
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),V0lo_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)),c_2Epair_2EUNCURRY_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Epair_2Eprod(A_27a,A_27a),tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0)))))))))))
                    & ! [V9i_2E0: mono_2Etyop_2Enum_2Enum,V10j_2E0: mono_2Etyop_2Enum_2Enum,V11x_2E0: u] :
                        ( ( ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V9i_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V11x_2E0))) )
                          & ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V10j_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V11x_2E0))) ) )
                       => ( V9i_2E0 = V10j_2E0 ) ) ) ) ) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LNIL,axiom,
    ! [A_27a: d,V0ll_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
      & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0)))))
      <=> ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LCONS,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0ll_2E0: u,V1h_2E0: u,V2t_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0)))))))
        <=> ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
            | ? [V3l_2E0: u] :
                ( ( s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0))) )
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) ) ) )
      & ! [V4h_2E0: u,V5t_2E0: u,V6ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V5t_2E0))),s(tyop_2Ellist_2Ellist(A_27b),V6ll_2E0)))))
        <=> ? [V7l_2E0: u] :
              ( ( s(tyop_2Ellist_2Ellist(A_27b),V6ll_2E0) = s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELCONS_2E2(s(A_27b,V4h_2E0),s(tyop_2Ellist_2Ellist(A_27b),V7l_2E0))) )
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27b),V5t_2E0),s(tyop_2Ellist_2Ellist(A_27b),V7l_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__LUNFOLD,axiom,
    ! [A_27a: d,A_27b: d,F0_2E0: u,F2_2E0: u,F1_2E0: u] :
      ( ! [V1ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
        <=> ( s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) )
     => ( ! [V1ll_2E0: u,V2f_2E0: u,V4n_2E0: u,V5x_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_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(A_27b,V4n_2E0))),s(A_27a,V5x_2E0)))))
          <=> ! [V6h_2E0: u,V7t_2E0: u] :
                ( ( s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V6h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0))) )
               => ( ( s(A_27a,V6h_2E0) = s(A_27a,V5x_2E0) )
                  & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V7t_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V4n_2E0))))))) ) ) )
       => ( ! [V1ll_2E0: u,V2f_2E0: u,V3v_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0))),s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Epair_2Epair__CASE_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),V3v_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0)))))) )
         => ! [V0n_2E0: u,V1ll_2E0: u,V2f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELUNFOLD_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0n_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0),s(A_27b,V0n_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool))),F1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(A_27b,A_27a))),V2f_2E0)))))) ) ) ) ) ).

tff(thm_2Ellist_2ELPREFIX__REFL,axiom,
    ! [A_27a: d,V0ll_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) ).

tff(thm_2Ellist_2ELPREFIX__ANTISYM,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))))) )
     => ( s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0) = s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0) ) ) ).

tff(thm_2Ellist_2ELPREFIX__TRANS,axiom,
    ! [A_27a: d,V0l3_2E0: u,V1l2_2E0: u,V2l1_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l3_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l3_2E0))))) ) ).

tff(thm_2Ellist_2ELPREFIX__fromList,axiom,
    ! [A_27a: d,F0_2E0: u,F1_2E0: u] :
      ( ! [V0l_2E0: u,V1ll_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))))
        <=> ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) ) )
     => ( ! [V0l_2E0: u,V2ys_2E0: u] : ( 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_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2EisPREFIX_2E2(s(tyop_2Elist_2Elist(A_27a),V0l_2E0),s(tyop_2Elist_2Elist(A_27a),V2ys_2E0)))) )
       => ! [V0l_2E0: u,V1ll_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2EtoList_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))),s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool)),F1_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) ) ) ) ).

tff(thm_2Ellist_2Eprefixes__lprefix__total,axiom,
    ! [A_27a: d,V0ll_2E0: u,V1l1_2E0: u,V2l2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0ll_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0)))))
        | p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l2_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0))))) ) ) ).

tff(thm_2Ellist_2ELTAKE__IMP__LDROP,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u,V2l1_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Ellist_2ELTAKE_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Elist_2Elist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))) )
     => ? [V3l2_2E0: u] :
          ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3l2_2E0))) )
          & ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V2l1_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V3l2_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0) ) ) ) ).

tff(thm_2Ellist_2ELDROP__EQ__LNIL,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ll_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0))) )
    <=> ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1ll_2E0)))) = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V0n_2E0) ) ) ).

tff(thm_2Ellist_2ELPREFIX__APPEND,axiom,
    ! [A_27a: d,V0l2_2E0: u,V1l1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELPREFIX_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0)))))
    <=> ? [V2ll_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),V0l2_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2ll_2E0))) ) ) ).

tff(thm_2Ellist_2ENOT__LFINITE__DROP__LFINITE,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l_2E0: u,V2t_2E0: u] :
      ( ( ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0)))))
        & ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) ) )
     => ~ p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))))) ) ).

tff(thm_2Ellist_2ELDROP__APPEND1,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1l2_2E0: u,V2l1_2E0: u,V3l_2E0: u] :
      ( ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0))) )
     => ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2l1_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V3l_2E0),s(tyop_2Ellist_2Ellist(A_27a),V1l2_2E0))))) ) ) ).

tff(thm_2Ellist_2ELDROP__fromList,axiom,
    ! [A_27a: d,V0ls_2E0: u,V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Earithmetic_2E_3C_3D_2E2(V1n_2E0,j_mono_2Etyop_2Enum_2Enum(s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V1n_2E0)),s(tyop_2Elist_2Elist(A_27a),V0ls_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0))) ) ).

tff(thm_2Ellist_2ELDROP__SUC,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1ls_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V0n_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1ls_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELDROP_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V1ls_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a))),c_2Ellist_2ELTL_2E0))) ) ).

tff(thm_2Ellist_2ELHD__LGENLIST,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0limopt_2E0))
        <=> ( V0limopt_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) ) )
     => ! [V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0limopt_2E0)))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0limopt_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))))))) ) ) ).

tff(thm_2Ellist_2ELTL__LGENLIST,axiom,
    ! [A_27a: d,F0_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29] :
      ( ! [V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0limopt_2E0))
        <=> ( V0limopt_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) ) )
     => ! [V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0limopt_2E0)))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(F0_2E0,V0limopt_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E0,V0limopt_2E0))))))))) ) ) ).

tff(thm_2Ellist_2Enumopt__BISIMULATION,axiom,
    ! [V0mopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1nopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
      ( ( V0mopt_2E0 = V1nopt_2E0 )
    <=> ? [V2R_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29] :
          ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V2R_2E0,V0mopt_2E0),V1nopt_2E0))
          & ! [V3m_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V4n_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] :
              ( p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V2R_2E0,V3m_2E0),V4n_2E0))
             => ( ( ( V3m_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) )
                  & ( V4n_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) ) )
                | ( ( V3m_2E0 != mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) )
                  & ( V4n_2E0 != mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) )
                  & p(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool(mono_2Eapp_2E2_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29(V2R_2E0,mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E0,V3m_2E0)),mono_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum(mono_2Ec_2Eprim__rec_2EPRE_2E0,V4n_2E0))) ) ) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__EQ__LNIL,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
      ( ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0n_2E0)))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      <=> ( V0n_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) ) )
      & ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0n_2E0)))) )
      <=> ( V0n_2E0 = mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0) ) ) ) ).

tff(thm_2Ellist_2ELFINITE__LGENLIST,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ellist_2ELFINITE_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0n_2E0))))))))
    <=> ( V0n_2E0 != mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum ) ) ).

tff(thm_2Ellist_2ELTL__HD__LTL__LHD,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V1h_2E0: u,V2t_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F1_2E0),s(A_27a,V1h_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2ESOME_2E1(s(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a),c_2Epair_2E_2C_2E2(s(tyop_2Ellist_2Ellist(A_27a),V2t_2E0),s(A_27a,V1h_2E0))))) )
     => ( ! [V0l_2E0: u,V1h_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))),s(A_27a,V1h_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F1_2E0),s(A_27a,V1h_2E0))))) )
       => ! [V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Ellist_2ELTL__HD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))) = s(tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)),c_2Eoption_2EOPTION__BIND_2E2(s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(tyop_2Epair_2Eprod(tyop_2Ellist_2Ellist(A_27a),A_27a)))),F0_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0l_2E0))))) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__SOME,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2ESUC_2E1(V1n_2E0)))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_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_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(V1n_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELGENLIST__SOME__compute,axiom,
    ! [A_27a: d,V0f_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      & ! [V1n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1n_2E0))))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_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_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2E_2D_2E2(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V1n_2E0)),mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0)))))))))) )
      & ! [V2n_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT2_2E1(V2n_2E0))))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V0f_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_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(V2n_2E0))))))))) ) ) ).

tff(thm_2Ellist_2ELNTH__LGENLIST,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V3lim0_2E0: mono_2Etyop_2Enum_2Enum] : ( s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V3lim0_2E0)))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(mono_2Ec_2Eprim__rec_2E_3C_2E2(V0n_2E0,V3lim0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0))) )
     => ! [V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2lim_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V2lim_2E0)))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Eoption__CASE_2E3(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V2lim_2E0)),s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)))),F0_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0))))) ) ) ).

tff(thm_2Ellist_2ELNTH__LMAP,axiom,
    ! [A_27a: d,A_27b: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u,V2l_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27b),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELNTH_2E2(s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)),s(tyop_2Ellist_2Ellist(A_27a),V2l_2E0))))) ) ).

tff(thm_2Ellist_2ELLENGTH__LGENLIST,axiom,
    ! [A_27a: d,V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1f_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0limopt_2E0))))))) = V0limopt_2E0 ) ).

tff(thm_2Ellist_2ELMAP__LGENLIST,axiom,
    ! [A_27a: d,A_27b: d,V0limopt_2E0: mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29,V1g_2E0: u,V2f_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELMAP_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Ellist_2Ellist(A_27b),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1g_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0limopt_2E0)))))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27b),V1g_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(V0limopt_2E0)))) ) ).

tff(thm_2Ellist_2ELGENLIST__EQ__CONS,axiom,
    ! [A_27a: d,V0t_2E0: u,V1h_2E0: u,V2f_2E0: u] :
      ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELCONS_2E2(s(A_27a,V1h_2E0),s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0))) )
    <=> ( ( s(A_27a,V1h_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V2f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0)))) )
        & ( s(tyop_2Ellist_2Ellist(A_27a),V0t_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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(mono_2Ec_2Earithmetic_2ENUMERAL_2E1(mono_2Ec_2Earithmetic_2EBIT1_2E1(mono_2Ec_2Earithmetic_2EZERO_2E0))))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))) ) ) ) ).

tff(thm_2Ellist_2ELGENLIST__CHUNK__GENLIST,axiom,
    ! [A_27a: d,V0n_2E0: mono_2Etyop_2Enum_2Enum,V1f_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),V1f_2E0),s(tyop_2Enum_2Enum,i_mono_2Etyop_2Enum_2Enum(V0n_2E0)))))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELGENLIST_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,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_2Earithmetic_2E_2B_2E1(V0n_2E0))))),s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),i_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum)))))) ) ).

tff(thm_2Ellist_2ELREPEAT__thm,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ).

tff(thm_2Ellist_2ELREPEAT__NIL,axiom,
    ! [A_27a: d] : ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) ) ).

tff(thm_2Ellist_2ELREPEAT__EQ__LNIL,axiom,
    ! [A_27a: d,V0l_2E0: u] :
      ( ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) )
      <=> ( s(tyop_2Elist_2Elist(A_27a),V0l_2E0) = s(tyop_2Elist_2Elist(A_27a),c_2Elist_2ENIL_2E0) ) )
      & ( ( s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELNIL_2E0) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(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) ) ) ) ).

tff(thm_2Ellist_2ELHD__LREPEAT,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Ellist_2ELHD_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) ) ).

tff(thm_2Ellist_2ELTL__LREPEAT,axiom,
    ! [A_27a: d,F0_2E0: u] :
      ( ! [V0l_2E0: u,V1t_2E0: u] : ( s(tyop_2Ellist_2Ellist(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0))) = s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELAPPEND_2E2(s(tyop_2Ellist_2Ellist(A_27a),V1t_2E0),s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) )
     => ! [V0l_2E0: u] : ( s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))) = s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Eoption_2EOPTION__MAP_2E2(s(tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Ellist_2Ellist(A_27a),tyop_2Ellist_2Ellist(A_27a))),F0_2E0),s(tyop_2Elist_2Elist(A_27a),V0l_2E0))),s(tyop_2Eoption_2Eoption(tyop_2Ellist_2Ellist(A_27a)),c_2Ellist_2ELTL_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2EfromList_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0))))))) ) ) ).

tff(thm_2Ellist_2ELLENGTH__LREPEAT,axiom,
    ! [A_27a: d,V0l_2E0: u] : ( j_mono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(s(tyop_2Eoption_2Eoption(tyop_2Enum_2Enum),c_2Ellist_2ELLENGTH_2E1(s(tyop_2Ellist_2Ellist(A_27a),c_2Ellist_2ELREPEAT_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))))) = mono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Enum_2Enum_29(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Elist_2ENULL_2E1(s(tyop_2Elist_2Elist(A_27a),V0l_2E0)))),mono_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Enum_2Enum(mono_2Ec_2Enum_2E0_2E0),mono_2Ec_2Eoption_2ENONE_2E0_2Emono_2Etyop_2Enum_2Enum) ) ).

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