%------------------------------------------------------------------------------
% File     : ITP065+4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : finite_map.ax [Gau19]
%          : HL4065+4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  532 ( 337 unt;   0 def)
%            Number of atoms       :  974 ( 617 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  476 (  34   ~;  13   |; 122   &)
%                                         (  88 <=>; 219  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :   21 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :  219 ( 219 usr; 111 con; 0-4 aty)
%            Number of variables   : 2591 (2563   !;  28   ?)
% SPC      : FOF_SAT_RFO_SEQ

% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
fof(reserved_2Eho_2Eboolext,axiom,
    ! [V0_2E0,V1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
      <=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
     => s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ) ).

fof(reserved_2Eho_2Etruth,axiom,
    p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ).

fof(reserved_2Eho_2Enotfalse,axiom,
    ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ).

fof(reserved_2Eho_2Ebool__cases__ax,axiom,
    ! [V0t_2E0] :
      ( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)
      | s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ) ).

fof(reserved_2Eho_2Ei__thm,axiom,
    ! [A_27a,V0x_2E0] : 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) ).

fof(reserved_2Eho_2Ek__thm,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : 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) ).

fof(reserved_2Eho_2Es__thm,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : 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))))) ).

fof(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        & p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
        | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_7E,axiom,
    ! [V0_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0))))
    <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ).

fof(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0_2E0,V1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0))))
    <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0))
       => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ).

fof(reserved_2Elogic_2E_3D,axiom,
    ! [A_27a,V0_2E0,V1_2E0] :
      ( p(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) ) ).

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

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

fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        & p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
        | p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
    ! [X0_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0))
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
    ! [X0_2E0,X1_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,X0_2E0))
       => p(s(tyop_2Emin_2Ebool,X1_2E0)) )
    <=> p(s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ).

fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] :
      ( s(A_27a,X0_2E0) = s(A_27a,X1_2E0)
    <=> p(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)))) ) ).

fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27a),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),c_2Elist_2EALL__DISTINCT_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X1_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2EASSOC_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Ebool),c_2Ecombin_2EASSOC_2E0),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X0_2E0))) ).

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

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

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

fof(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) ).

fof(arityeq1_2Ec_2Ecombin_2ECOMM_2E1_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),tyop_2Emin_2Ebool),c_2Ecombin_2ECOMM_2E0),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Efinite__map_2EFCARD_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum),c_2Efinite__map_2EFCARD_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : 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))) ).

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

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

fof(arityeq2_2Ec_2Efinite__map_2EFMAP__MAP2_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFMAP__MAP2_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFMAP__MAP2_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) ).

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Efinite__map_2Ef__o_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))),c_2Efinite__map_2Ef__o_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2Ef__o__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o__f_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))),c_2Efinite__map_2Ef__o__f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2Eo__f_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27c))),c_2Efinite__map_2Eo__f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).

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

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

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

fof(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Efinite__map_2EMAP__KEYS_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) ).

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

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

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq1_2Ec_2Epred__set_2EGSPEC_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a,X0_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)),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))) ).

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EFINITE_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))) ).

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

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

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

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

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

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

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

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

fof(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,X0_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Esum_2EINR_2E0),s(tyop_2Eone_2Eone,X0_2E0))) ).

fof(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27b_20mono_2Etyop_2Eone_2Eone,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Esum_2EISL_2E0),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27a),X0_2E0))) = 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))) ).

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(A_27b),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(A_27b),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27c_29,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27c)),X0_2E0))) ).

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

fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : 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))) ).

fof(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : 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))) ).

fof(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Enum_2ESUC_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

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

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

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

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

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

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

fof(arityeq1_2Ec_2Efinite__map_2Eis__fmap_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),c_2Efinite__map_2Eis__fmap_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),X0_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(A_27a,c_2Elist_2EEL_2E2(s(tyop_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,X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))) ).

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

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

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

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),c_2Earithmetic_2E_2B_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,X0_2E0),s(tyop_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,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27b,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27b,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27b,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Ebool,X1_2E0))) = s(tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Epair_2Eprod(A_27c,tyop_2Emin_2Ebool))),c_2Epair_2E_2C_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27a,X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(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)),c_2Eprim__rec_2E_3C_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))) ).

fof(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a,A_27b,X0_2E0] : s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Enum_2Enum),c_2Elist_2ELENGTH_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),X0_2E0))) ).

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

fof(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : 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))) ).

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

fof(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2EDISJOINT_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) ).

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

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

fof(arityeq1_2Ec_2Epred__set_2ECOMPL_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Epred__set_2ECOMPL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

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

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

fof(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : 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))) ).

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

fof(arityeq2_2Ec_2Efinite__map_2EDRESTRICT_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),c_2Efinite__map_2EDRESTRICT_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,X0_2E0),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),A_27b)),c_2Elist_2EEL_2E0),s(tyop_2Enum_2Enum,X0_2E0))),s(tyop_2Elist_2Elist(A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Elist_2Elist(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Elist_2Elist(A_27b))),c_2Elist_2EMAP_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).

fof(arityeq2_2Ec_2Elist_2EEVERY_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2EEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Elist_2EEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).

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

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

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

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

fof(arityeq2_2Ec_2Efinite__map_2EFDOM_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFDOM_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(A_27a,X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Efinite__map_2EFDOM_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2EFEVERY_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Efinite__map_2EFEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2EFEVERY_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Efinite__map_2EFEVERY_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27c),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),X1_2E0))) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27b,A_27c,X0_2E0,X1_2E0] : 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))) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Elist_2Elist_28A_27d_29_20mono_2Etyop_2Elist_2Elist_28A_27e_29,axiom,
    ! [A_27d,A_27e,X0_2E0,X1_2E0] : s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)),c_2Epair_2E_2C_2E2(s(tyop_2Elist_2Elist(A_27d),X0_2E0),s(tyop_2Elist_2Elist(A_27e),X1_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27d),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27e),tyop_2Epair_2Eprod(tyop_2Elist_2Elist(A_27d),tyop_2Elist_2Elist(A_27e)))),c_2Epair_2E_2C_2E0),s(tyop_2Elist_2Elist(A_27d),X0_2E0))),s(tyop_2Elist_2Elist(A_27e),X1_2E0))) ).

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

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

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

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

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

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

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

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

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

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27c,axiom,
    ! [A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(A_27c,X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),X1_2E0))) ).

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

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

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27b_2CA_27a_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2EIN_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),tyop_2Emin_2Ebool),X1_2E0))) ).

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

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

fof(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28A_27a_2CA_27b_29_2Ctyop_2Emin_2Efun_28tyop_2Efinite__map_2Efmap_28A_27a_2CA_27c_29_2Ctyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),X1_2E0))) ).

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

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

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

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

fof(arityeq2_2Ec_2Epred__set_2ELINV_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Epred__set_2ELINV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2EMAP__KEYS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),X1_2E0))) = s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a))),c_2Efinite__map_2EMAP__KEYS_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),X1_2E0))) ).

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

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

fof(arityeq1_2Ec_2Eoption_2Esome_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2Esome_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2Esome_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ).

fof(arityeq2_2Ec_2Esorting_2EPERM_2E2_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Esorting_2EPERM_2E2(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),tyop_2Emin_2Ebool)),c_2Esorting_2EPERM_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X0_2E0))),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Efinite__map_2ESUBMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Efinite__map_2ESUBMAP_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))) ).

fof(arityeq2_2Ec_2Efinite__map_2ESUBMAP_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c,A_27d,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27c,A_27d),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27d),tyop_2Emin_2Ebool)),c_2Efinite__map_2ESUBMAP_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27d),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27c,A_27d),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Epred__set_2ESUBSET_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))) ).

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

fof(arityeq2_2Ec_2Epred__set_2ESUM__IMAGE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0] : s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum)),c_2Epred__set_2ESUM__IMAGE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))) ).

fof(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29_29_20mono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),tyop_2Emin_2Ebool)),c_2Ebool_2ETYPE__DEFINITION_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),X1_2E0))) ).

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

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

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

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

fof(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0] : 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))) ).

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

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

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

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

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

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

fof(arityeq2_2Ec_2Efinite__map_2Efmap__inverse_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__inverse_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool)),c_2Efinite__map_2Efmap__inverse_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0))) ).

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

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

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

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

fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ).

fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27a,X1_2E0),s(A_27a,X2_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(A_27b,X1_2E0),s(A_27b,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27a_2CA_27b_29,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Efinite__map_2Efmap_28A_27b_2CA_27c_29,axiom,
    ! [A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Efinite__map_2Efmap(A_27b,A_27c)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),X2_2E0))) ).

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

fof(arityeq3_2Ec_2Epred__set_2EINJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EINJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EBIT1_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
    ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Enum_2Enum,X1_2E0),s(tyop_2Enum_2Enum,X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(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)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Enum_2Enum,X1_2E0))),s(tyop_2Enum_2Enum,X2_2E0))) ).

fof(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
    ! [X0_2E0] : s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,X0_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2ENUMERAL_2E0),s(tyop_2Enum_2Enum,X0_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
    ! [A_27a,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2ECOND_2E3(s(tyop_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,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
    ! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2Ctyop_2Eone_2Eone_29,axiom,
    ! [A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,X0_2E0),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X1_2E0),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X2_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),c_2Ebool_2ECOND_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X1_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),X2_2E0))) ).

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

fof(arityeq1_2Ec_2Ecombin_2EC_2E1_2Emono_2EA_27b_20mono_2EA_27b_20mono_2EA_27b,axiom,
    ! [A_27b,X0_2E0] : s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),c_2Ecombin_2EC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0))) ).

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

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

fof(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b,A_27c,X0_2E0] : s(tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2EK_2E1(s(A_27b,X0_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27b),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27b)),c_2Ecombin_2EK_2E0),s(A_27b,X0_2E0))) ).

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

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

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

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

fof(arityeq3_2Ec_2Elist_2ELIST__REL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Elist_2ELIST__REL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Elist_2Elist(A_27a),X1_2E0),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Ebool))),c_2Elist_2ELIST__REL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Elist_2Elist(A_27a),X1_2E0))),s(tyop_2Elist_2Elist(A_27b),X2_2E0))) ).

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

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

fof(arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Eoption_2EOPTREL_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Ebool))),c_2Eoption_2EOPTREL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Eoption_2Eoption(A_27a),X1_2E0))),s(tyop_2Eoption_2Eoption(A_27b),X2_2E0))) ).

fof(arityeq3_2Ec_2Efinite__map_2Efmap__EQ__UPTO_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__EQ__UPTO_2E3(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Efinite__map_2Efmap__EQ__UPTO_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ).

fof(arityeq3_2Ec_2Efinite__map_2Efmap__rel_2E3_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Efinite__map_2Efmap__rel_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),X2_2E0))) ).

fof(arityeq3_2Ec_2Efinite__map_2Efmap__rel_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a,A_27b,A_27c,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27c,A_27b),tyop_2Emin_2Ebool))),c_2Efinite__map_2Efmap__rel_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),X2_2E0))) ).

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

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

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

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

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

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

fof(arityeq3_2Ec_2Efinite__map_2Efmap__size_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Enum_2Enum,c_2Efinite__map_2Efmap__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) = s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Enum_2Enum))),c_2Efinite__map_2Efmap__size_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),X1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),X2_2E0))) ).

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

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

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

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

fof(thm_2Efinite__map_2Efmap__inverse__def,axiom,
    ! [A_27a,A_27b,V0m1_2E0,V1m2_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__inverse_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0m1_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1m2_2E0))))
    <=> ! [V2k_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2k_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0m1_2E0))))))
         => ? [V3v_2E0] :
              ( s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0m1_2E0),s(A_27a,V2k_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V3v_2E0)))
              & s(tyop_2Eoption_2Eoption(A_27a),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1m2_2E0),s(A_27b,V3v_2E0))) = s(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(s(A_27a,V2k_2E0))) ) ) ) ).

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

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

fof(thm_2Efinite__map_2ESUBMAP__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
    <=> ! [V2x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
         => ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))))
            & s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) ) ) ) ).

fof(thm_2Efinite__map_2EFCARD__DEF,axiom,
    ! [A_27a,A_27b,V0fm_2E0] : s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))))) ).

fof(thm_2Efinite__map_2EFDOM__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1x_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFDOM_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Emin_2Ebool,c_2Esum_2EISL_2E1(s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Efinite__map_2Efmap__REP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))))) ).

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

fof(thm_2Efinite__map_2EFEMPTY__DEF,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0a_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0),s(A_27a,V0a_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efmap__ABS_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0))) ) ).

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

fof(thm_2Efinite__map_2Efmap__ISO__DEF,axiom,
    ! [A_27a,A_27b] :
      ( ! [V0a_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efmap__ABS_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efinite__map_2Efmap__REP_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0a_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0a_2E0)
      & ! [V1r_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1r_2E0))))
        <=> s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),c_2Efinite__map_2Efmap__REP_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efmap__ABS_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1r_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1r_2E0) ) ) ).

fof(thm_2Efinite__map_2Efmap__TY__DEF,axiom,
    ! [A_27a,A_27b] :
    ? [V0rep_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ebool_2ETYPE__DEFINITION_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),c_2Efinite__map_2Eis__fmap_2E0),s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),V0rep_2E0)))) ).

fof(thm_2Efinite__map_2Eis__fmap__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V7x_2E0,V5a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V7x_2E0))),s(A_27a,V5a_2E0))))
        <=> s(A_27a,V7x_2E0) = s(A_27a,V5a_2E0) )
     => ! [V0x_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V0x_2E0))))
        <=> ! [V1is__fmap_27_2E0] :
              ( ! [V2a0_2E0] :
                  ( ( ! [V3x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2a0_2E0),s(A_27a,V3x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
                    | ? [V4f_2E0,V5a_2E0,V6b_2E0] :
                        ( ! [V7x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2a0_2E0),s(A_27a,V7x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V7x_2E0))),s(A_27a,V5a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V6b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V4f_2E0),s(A_27a,V7x_2E0)))))
                        & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V1is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V4f_2E0)))) ) )
                 => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V1is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2a0_2E0)))) )
             => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V1is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V0x_2E0)))) ) ) ) ).

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

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

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

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

fof(thm_2Efinite__map_2EFUN__FMAP__DEF,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1P_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
     => ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)
        & ! [V2x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
           => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) ) ) ) ).

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

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

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

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

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

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

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

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

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

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

fof(thm_2Efinite__map_2Efmap__size__def,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V0kz_2E0,V1vz_2E0,V2fm_2E0,V3k_2E0] : s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0kz_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1vz_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0))),s(A_27a,V3k_2E0))) = s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0kz_2E0),s(A_27a,V3k_2E0))),s(tyop_2Enum_2Enum,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1vz_2E0),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0),s(A_27a,V3k_2E0)))))))
     => ! [V0kz_2E0,V1vz_2E0,V2fm_2E0] : s(tyop_2Enum_2Enum,c_2Efinite__map_2Efmap__size_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0kz_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1vz_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0))) = s(tyop_2Enum_2Enum,c_2Epred__set_2ESUM__IMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V0kz_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Enum_2Enum),V1vz_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0))))) ) ).

fof(thm_2Efinite__map_2Efevery__funion,axiom,
    ! [A_27a,A_27b,V0P_2E0,V1m1_2E0,V2m2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m1_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2m2_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2m2_2E0)))))) ) ).

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

fof(thm_2Efinite__map_2Edisjoint__drestrict,axiom,
    ! [A_27a,A_27b,V0s_2E0,V1m_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m_2E0))))))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1m_2E0) ) ).

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

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

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

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

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

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

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

fof(thm_2Efinite__map_2Efmap__rel__sym,axiom,
    ! [A_27a,A_27b,V0R_2E0] :
      ( ! [V1x_2E0,V2y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V1x_2E0)))) )
     => ! [V3x_2E0,V4y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V3x_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V4y_2E0))))
         => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V4y_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V3x_2E0)))) ) ) ).

fof(thm_2Efinite__map_2Efmap__rel__trans,axiom,
    ! [A_27a,A_27b,V0R_2E0] :
      ( ! [V1x_2E0,V2y_2E0,V3z_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_2E0))))
            & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2y_2E0))),s(A_27a,V3z_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V3z_2E0)))) )
     => ! [V4x_2E0,V5y_2E0,V6z_2E0] :
          ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V4x_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V5y_2E0))))
            & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V5y_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V6z_2E0)))) )
         => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V4x_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V6z_2E0)))) ) ) ).

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

fof(thm_2Efinite__map_2EDRESTRICT__SUBSET,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2s_2E0,V3t_2E0] :
      ( ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) )
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))) ) ).

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

fof(thm_2Efinite__map_2EFRANGE__DRESTRICT__SUBSET,axiom,
    ! [A_27a,A_27b,V0s_2E0,V1fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0)))))) ).

fof(thm_2Efinite__map_2EIN__FRANGE__DOMSUB__suff,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1fm_2E0,V2P_2E0] :
      ( ! [V3v_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0))))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3v_2E0)))) )
     => ! [V4v_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0),s(A_27b,V0k_2E0))))))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4v_2E0)))) ) ) ).

fof(thm_2Efinite__map_2EFRANGE__DOMSUB__SUBSET,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0),s(A_27b,V0k_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0)))))) ).

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

fof(thm_2Efinite__map_2EFRANGE__FUNION__SUBSET,axiom,
    ! [A_27a,A_27b,V0f2_2E0,V1f1_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f2_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f2_2E0)))))))) ).

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

fof(thm_2Efinite__map_2EFRANGE__FUPDATE__LIST__SUBSET,axiom,
    ! [A_27a,A_27b,V0ls_2E0,V1fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ls_2E0))))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ls_2E0)))))))))) ).

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

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

fof(thm_2Efinite__map_2EFUPDATE__LIST__ALL__DISTINCT__REVERSE,axiom,
    ! [A_27a,A_27b,V0ls_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E1(s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ls_2E0))))))
     => ! [V1fm_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),c_2Elist_2EREVERSE_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ls_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0ls_2E0))) ) ).

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

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

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

fof(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__HO__THM,axiom,
    ! [A_27a,A_27b,V0P_2E0,V1f_2E0,V2kvl_2E0,V3k_2E0] :
      ( ( ? [V4n_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0))))))
            & s(A_27b,V3k_2E0) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0)))))
            & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27a),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0))))))))
            & ! [V5m_2E0] :
                ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V5m_2E0))))
                  & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0)))))) )
               => s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0))))) != s(A_27b,V3k_2E0) ) )
        | ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,V3k_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E1(s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27a),A_27b),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0))))))))
          & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f_2E0),s(A_27b,V3k_2E0)))))) ) )
     => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),V2kvl_2E0))),s(A_27b,V3k_2E0)))))) ) ).

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

fof(thm_2Efinite__map_2EDRESTRICT__FUNION__SUBSET,axiom,
    ! [A_27a,A_27b,V0s2_2E0,V1s1_2E0,V2g_2E0,V3f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))))
     => ? [V4h_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V4h_2E0))) ) ).

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

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

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

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

fof(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP__gen,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2s_2E0,V3t_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2s_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3t_2E0)))))) ) ).

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

fof(thm_2Efinite__map_2EDOMSUB__SUBMAP,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2x_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
        & ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0)))))) ) ).

fof(thm_2Efinite__map_2ESUBMAP__DOMSUB__gen,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2k_2E0] : s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2k_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))) = s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2k_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2k_2E0))))) ).

fof(thm_2Efinite__map_2ESUBMAP__mono__FUPDATE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2x_2E0,V3y_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(A_27b,V3y_2E0)))))))) ) ).

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

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

fof(thm_2Efinite__map_2EDRESTRICT__SUBSET__SUBMAP,axiom,
    ! [A_27a,A_27b,V0s2_2E0,V1s1_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s1_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s2_2E0)))))) ) ).

fof(thm_2Efinite__map_2EDRESTRICT__SUBMAP__gen,axiom,
    ! [A_27a,A_27b,V0g_2E0,V1f_2E0,V2P_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0)))) ) ).

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

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

fof(thm_2Efinite__map_2EFRANGE__FUPDATE__SUBSET,axiom,
    ! [A_27a,A_27b,V0kv_2E0,V1fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0),s(tyop_2Epair_2Eprod(A_27b,A_27a),V0kv_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,c_2Epair_2ESND_2E1(s(tyop_2Epair_2Eprod(A_27b,A_27a),V0kv_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0)))))))) ).

fof(thm_2Efinite__map_2EIN__FRANGE__DRESTRICT__suff,axiom,
    ! [A_27a,A_27b,V0s_2E0,V1fm_2E0,V2P_2E0] :
      ( ! [V3v_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0))))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V3v_2E0)))) )
     => ! [V4v_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V4v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1fm_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V0s_2E0))))))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0),s(A_27a,V4v_2E0)))) ) ) ).

fof(thm_2Efinite__map_2EFUNION__ASSOC,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2h_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0))) ).

fof(thm_2Efinite__map_2EFUNION__COMM,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) ) ).

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

fof(thm_2Efinite__map_2EFUNION__EQ__IMPL,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2f3_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0))))))
        & s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0) )
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0))) ) ).

fof(thm_2Efinite__map_2EFUNION__EQ,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2f3_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))))))
        & p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0)))))) )
     => ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0)))
      <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0) ) ) ).

fof(thm_2Efinite__map_2EFEMPTY__SUBMAP,axiom,
    ! [A_27a,A_27b,V0h_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0h_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0))))
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0h_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) ) ).

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

fof(thm_2Efinite__map_2ESUBMAP__FUNION,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2f3_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))))
        | ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0)))) ) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f3_2E0)))))) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(thm_2Efinite__map_2EFUPD11__SAME__BASE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1k1_2E0,V2v1_2E0,V3k2_2E0,V4v2_2E0] :
      ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1k1_2E0),s(A_27b,V2v1_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3k2_2E0),s(A_27b,V4v2_2E0)))))
    <=> ( ( s(A_27a,V1k1_2E0) = s(A_27a,V3k2_2E0)
          & s(A_27b,V2v1_2E0) = s(A_27b,V4v2_2E0) )
        | ( s(A_27a,V1k1_2E0) != s(A_27a,V3k2_2E0)
          & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1k1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
          & p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3k2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
          & s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1k1_2E0),s(A_27b,V2v1_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)
          & s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3k2_2E0),s(A_27b,V4v2_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) ) ) ) ).

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

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

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

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

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

fof(thm_2Efinite__map_2EFUPDATE__LIST__APPLY__MEM,axiom,
    ! [A_27a,A_27b,V0kvl_2E0,V1f_2E0,V2k_2E0,V3v_2E0,V4n_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0))))))
        & s(A_27a,V2k_2E0) = s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0)))))
        & s(A_27b,V3v_2E0) = s(A_27b,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Elist_2Elist(A_27b),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b),c_2Epair_2ESND_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0)))))
        & ! [V5m_2E0] :
            ( ( p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V4n_2E0),s(tyop_2Enum_2Enum,V5m_2E0))))
              & p(s(tyop_2Emin_2Ebool,c_2Eprim__rec_2E_3C_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E1(s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0)))))) )
           => s(A_27a,c_2Elist_2EEL_2E2(s(tyop_2Enum_2Enum,V5m_2E0),s(tyop_2Elist_2Elist(A_27a),c_2Elist_2EMAP_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a),c_2Epair_2EFST_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0))))) != s(A_27a,V2k_2E0) ) )
     => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE__LIST_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27a,A_27b)),V0kvl_2E0))),s(A_27a,V2k_2E0))) = s(A_27b,V3v_2E0) ) ).

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

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

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

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

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

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

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

fof(thm_2Efinite__map_2ESUBMAP__TRANS,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0,V2h_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h_2E0)))) ) ).

fof(thm_2Efinite__map_2ESUBMAP__ANTISYM,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))) )
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0) ) ).

fof(thm_2Efinite__map_2ESUBMAP__REFL,axiom,
    ! [A_27a,A_27b,V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))) ).

fof(thm_2Efinite__map_2ESUBMAP__FEMPTY,axiom,
    ! [A_27a,A_27b,V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))) ).

fof(thm_2Efinite__map_2Efmap__EXT,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0)
    <=> ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0)))
        & ! [V2x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
           => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) ) ) ) ).

fof(thm_2Efinite__map_2Efmap__EQ__THM,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0)))
        & ! [V2x_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
           => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) ) )
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0) ) ).

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

fof(thm_2Efinite__map_2ENOT__FDOM__FAPPLY__FEMPTY,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1x_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
     => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V1x_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(A_27a,V1x_2E0))) ) ).

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

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

fof(thm_2Efinite__map_2EFCARD__SUC,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1n_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2ESUC_2E1(s(tyop_2Enum_2Enum,V1n_2E0)))
    <=> ? [V2f_27_2E0,V3x_2E0,V4y_2E0] :
          ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_27_2E0))))))
          & s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_27_2E0))) = s(tyop_2Enum_2Enum,V1n_2E0)
          & s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2f_27_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(A_27b,V4y_2E0))))) ) ) ).

fof(thm_2Efinite__map_2EFCARD__0__FEMPTY,axiom,
    ! [A_27a,A_27b,V0f_2E0] :
      ( s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0)
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) ) ).

fof(thm_2Efinite__map_2EFCARD__FUPDATE,axiom,
    ! [A_27a,A_27b,V0fm_2E0,V1a_2E0,V2b_2E0] : s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0))))))) = s(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))))),s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))),s(tyop_2Enum_2Enum,c_2Earithmetic_2E_2B_2E2(s(tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E1(s(tyop_2Enum_2Enum,c_2Earithmetic_2EZERO_2E0))))),s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))))))) ).

fof(thm_2Efinite__map_2EFCARD__FEMPTY,axiom,
    ! [A_27a,A_27b] : s(tyop_2Enum_2Enum,c_2Efinite__map_2EFCARD_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0))) = s(tyop_2Enum_2Enum,c_2Enum_2E0_2E0) ).

fof(thm_2Efinite__map_2EFDOM__FINITE,axiom,
    ! [A_27a,A_27b,V0fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0)))))) ).

fof(thm_2Efinite__map_2EFDOM__F__FEMPTY1,axiom,
    ! [A_27a,A_27b,V0f_2E0] :
      ( ! [V1a_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1a_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) ) ).

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

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

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

fof(thm_2Efinite__map_2EFDOM__EQ__FDOM__FUPDATE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
     => ! [V2y_2E0] : s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1x_2E0),s(A_27b,V2y_2E0))))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) ) ).

fof(thm_2Efinite__map_2ENOT__EQ__FEMPTY__FUPDATE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1a_2E0,V2b_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) != s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0))))) ).

fof(thm_2Efinite__map_2EFAPPLY__FUPDATE__THM,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V3x_2E0,V1a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V3x_2E0))),s(A_27a,V1a_2E0))))
        <=> s(A_27a,V3x_2E0) = s(A_27a,V1a_2E0) )
     => ! [V0f_2E0,V1a_2E0,V2b_2E0,V3x_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1a_2E0),s(A_27b,V2b_2E0))))),s(A_27a,V3x_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V3x_2E0))),s(A_27a,V1a_2E0))),s(A_27b,V2b_2E0),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))))) ) ).

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

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

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

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

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

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

fof(thm_2Efinite__map_2Eis__fmap__cases,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V5x_2E0,V3a_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))))
        <=> s(A_27a,V5x_2E0) = s(A_27a,V3a_2E0) )
     => ! [V0a0_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V0a0_2E0))))
        <=> ( ! [V1x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V0a0_2E0),s(A_27a,V1x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
            | ? [V2f_2E0,V3a_2E0,V4b_2E0] :
                ( ! [V5x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V0a0_2E0),s(A_27a,V5x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V4b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0),s(A_27a,V5x_2E0)))))
                & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))) ) ) ) ) ).

fof(thm_2Efinite__map_2Eis__fmap__strongind,axiom,
    ! [A_27a,A_27b,F0_2E0,F2_2E0,F1_2E0] :
      ( ! [V1a_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0),s(A_27a,V1a_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
     => ( ! [V5x_2E0,V3a_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))))
          <=> s(A_27a,V5x_2E0) = s(A_27a,V3a_2E0) )
       => ( ! [V3a_2E0,V4b_2E0,V2f_2E0,V5x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))),s(A_27a,V5x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V4b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0),s(A_27a,V5x_2E0)))))
         => ! [V0is__fmap_27_2E0] :
              ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0))))
                & ! [V2f_2E0,V3a_2E0,V4b_2E0] :
                    ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))))
                      & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))) )
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))))) ) )
             => ! [V6a0_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0))))
                 => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0)))) ) ) ) ) ) ).

fof(thm_2Efinite__map_2Eis__fmap__ind,axiom,
    ! [A_27a,A_27b,F0_2E0,F2_2E0,F1_2E0] :
      ( ! [V1a_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0),s(A_27a,V1a_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
     => ( ! [V5x_2E0,V3a_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))))
          <=> s(A_27a,V5x_2E0) = s(A_27a,V3a_2E0) )
       => ( ! [V3a_2E0,V4b_2E0,V2f_2E0,V5x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))),s(A_27a,V5x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V5x_2E0))),s(A_27a,V3a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V4b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0),s(A_27a,V5x_2E0)))))
         => ! [V0is__fmap_27_2E0] :
              ( ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0))))
                & ! [V2f_2E0,V3a_2E0,V4b_2E0] :
                    ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0))))
                   => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V3a_2E0))),s(A_27b,V4b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V2f_2E0)))))) ) )
             => ! [V6a0_2E0] :
                  ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0))))
                 => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Ebool),V0is__fmap_27_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V6a0_2E0)))) ) ) ) ) ) ).

fof(thm_2Efinite__map_2Eis__fmap__rules,axiom,
    ! [A_27a,A_27b,F0_2E0,F2_2E0,F1_2E0] :
      ( ! [V0a_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0),s(A_27a,V0a_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINR_2E1(s(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0)))
     => ( ! [V4x_2E0,V2a_2E0] :
            ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V2a_2E0))))
          <=> s(A_27a,V4x_2E0) = s(A_27a,V2a_2E0) )
       => ( ! [V2a_2E0,V3b_2E0,V1f_2E0,V4x_2E0] : s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1f_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0),s(A_27a,V4x_2E0))),s(A_27a,V2a_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),c_2Esum_2EINL_2E1(s(A_27b,V3b_2E0))),s(tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1f_2E0),s(A_27a,V4x_2E0)))))
         => ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),F0_2E0))))
            & ! [V1f_2E0,V2a_2E0,V3b_2E0] :
                ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1f_2E0))))
               => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Eis__fmap_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)))),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone))))),F1_2E0),s(A_27a,V2a_2E0))),s(A_27b,V3b_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Esum_2Esum(A_27b,tyop_2Eone_2Eone)),V1f_2E0)))))) ) ) ) ) ) ).

fof(thm_2Efinite__map_2EFUNION__FEMPTY__1,axiom,
    ! [A_27a,A_27b,V0g_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0) ).

fof(thm_2Efinite__map_2EFUNION__FEMPTY__2,axiom,
    ! [A_27a,A_27b,V0f_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) ).

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

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

fof(thm_2Efinite__map_2EEQ__FDOM__SUBMAP,axiom,
    ! [A_27a,A_27b,V0g_2E0,V1f_2E0] :
      ( s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0)
    <=> ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0))))
        & s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0g_2E0))) ) ) ).

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

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

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

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

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

fof(thm_2Efinite__map_2ENOT__FDOM__DRESTRICT,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1x_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))))))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EINSERT_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0) ) ).

fof(thm_2Efinite__map_2EDRESTRICT__SUBMAP,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1P_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))) ).

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

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

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

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

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

fof(thm_2Efinite__map_2ESUBMAP__DRESTRICT,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1P_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0)))) ).

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

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

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

fof(thm_2Efinite__map_2ESUBMAP__DOMSUB,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(A_27a,V0k_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0)))) ).

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

fof(thm_2Efinite__map_2EDOMSUB__NOT__IN__DOM,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1fm_2E0] :
      ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0k_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0))))))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(A_27a,V0k_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0) ) ).

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

fof(thm_2Efinite__map_2EDOMSUB__COMMUTES,axiom,
    ! [A_27a,A_27b,V0k2_2E0,V1k1_2E0,V2fm_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V0k2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2fm_2E0),s(A_27a,V0k2_2E0))),s(A_27a,V1k1_2E0))) ).

fof(thm_2Efinite__map_2EDOMSUB__IDEM,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1fm_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(A_27a,V0k_2E0))),s(A_27a,V0k_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0),s(A_27a,V0k_2E0))) ).

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

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

fof(thm_2Efinite__map_2EDOMSUB__FLOOKUP__THM,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1k1_2E0,V2k2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))))
        <=> s(A_27a,V1k1_2E0) = s(A_27a,V2k2_2E0) )
     => ! [V0fm_2E0,V1k1_2E0,V2k2_2E0] : s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0),s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))))) ) ).

fof(thm_2Efinite__map_2EDOMSUB__FLOOKUP__NEQ,axiom,
    ! [A_27a,A_27b,V0fm_2E0,V1k1_2E0,V2k2_2E0] :
      ( s(A_27a,V1k1_2E0) != s(A_27a,V2k2_2E0)
     => s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))) ) ).

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

fof(thm_2Efinite__map_2EDOMSUB__FAPPLY__THM,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1k1_2E0,V2k2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))))
        <=> s(A_27a,V1k1_2E0) = s(A_27a,V2k2_2E0) )
     => ! [V0fm_2E0,V1k1_2E0,V2k2_2E0] : s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))) = s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(A_27a,V2k2_2E0))),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))))) ) ).

fof(thm_2Efinite__map_2EDOMSUB__FAPPLY__NEQ,axiom,
    ! [A_27a,A_27b,V0fm_2E0,V1k1_2E0,V2k2_2E0] :
      ( s(A_27a,V1k1_2E0) != s(A_27a,V2k2_2E0)
     => s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))) = s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))) ) ).

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

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

fof(thm_2Efinite__map_2EDOMSUB__FUPDATE__THM,axiom,
    ! [A_27a,A_27b,F0_2E0] :
      ( ! [V1k1_2E0,V2k2_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))))
        <=> s(A_27a,V1k1_2E0) = s(A_27a,V2k2_2E0) )
     => ! [V0fm_2E0,V1k1_2E0,V2k2_2E0,V3v_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1k1_2E0),s(A_27b,V3v_2E0))))),s(A_27a,V2k2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(A_27a,V1k1_2E0))),s(A_27a,V2k2_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(A_27a,V2k2_2E0))),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V1k1_2E0),s(A_27b,V3v_2E0))))))) ) ).

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

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

fof(thm_2Efinite__map_2EDOMSUB__FEMPTY,axiom,
    ! [A_27a,A_27b,V0k_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0),s(A_27a,V0k_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0) ).

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

fof(thm_2Efinite__map_2EFINITE__PRED__11,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V0g_2E0,V3f_2E0,V4x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3f_2E0))),s(A_27a,V4x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V4x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V4x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3f_2E0)))))))
     => ! [V0g_2E0] :
          ( ! [V1x_2E0,V2y_2E0] :
              ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V1x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0),s(A_27a,V2y_2E0)))
            <=> s(A_27a,V1x_2E0) = s(A_27a,V2y_2E0) )
         => ! [V3f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V0g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V3f_2E0)))))))) ) ) ).

fof(thm_2Efinite__map_2EFAPPLY__f__o,axiom,
    ! [A_27a,A_27b,A_27c,F0_2E0] :
      ( ! [V1g_2E0,V0f_2E0,V2x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0)))))))
     => ! [V0f_2E0,V1g_2E0] :
          ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))))))))
         => ! [V3x_2E0] :
              ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))))))
             => s(A_27c,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V3x_2E0))) = s(A_27c,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3x_2E0))))) ) ) ) ).

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

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

fof(thm_2Efinite__map_2EFDOM__f__o,axiom,
    ! [A_27a,A_27b,A_27c,F1_2E0,F0_2E0] :
      ( ! [V1g_2E0,V0f_2E0,V3x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))),s(A_27a,V3x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0)))))))
     => ( ! [V1g_2E0,V0f_2E0,V2x_2E0] : s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))),s(A_27a,V2x_2E0))) = s(tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool),c_2Epair_2E_2C_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0)))))))
       => ! [V0f_2E0,V1g_2E0] :
            ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))))))))
           => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EGSPEC_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27b,A_27c),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(A_27a,tyop_2Emin_2Ebool)))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0))))) ) ) ) ).

fof(thm_2Efinite__map_2EFLOOKUP__FUN__FMAP,axiom,
    ! [A_27a,A_27b,V0k_2E0,V1f_2E0,V2P_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))))
     => s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(A_27a,V0k_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0k_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2P_2E0))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1f_2E0),s(A_27a,V0k_2E0))))),s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ENONE_2E0))) ) ).

fof(thm_2Efinite__map_2EFDOM__FMAP,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1s_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))
     => s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0))))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1s_2E0) ) ).

fof(thm_2Efinite__map_2EFRANGE__FMAP,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1P_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))
     => s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUN__FMAP_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))) ) ).

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

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

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

fof(thm_2Efinite__map_2EFRANGE__FUNION,axiom,
    ! [A_27a,A_27b,V0fm2_2E0,V1fm1_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm2_2E0))))))
     => s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm2_2E0))))) = s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNION_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm2_2E0))))) ) ).

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

fof(thm_2Efinite__map_2Eo__f__FRANGE,axiom,
    ! [A_27a,A_27b,A_27c,V0x_2E0,V1g_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1g_2E0))))))
     => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f_2E0),s(A_27a,V0x_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V2f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V1g_2E0)))))))) ) ).

fof(thm_2Efinite__map_2EFINITE__FRANGE,axiom,
    ! [A_27a,A_27b,V0fm_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0)))))) ).

fof(thm_2Efinite__map_2ESUBMAP__FRANGE,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Efinite__map_2EFRANGE_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0)))))) ) ).

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

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

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

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

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

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

fof(thm_2Efinite__map_2Eo__f__FAPPLY,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))))
     => s(A_27c,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Eo__f_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0),s(A_27b,c_2Efinite__map_2EFAPPLY_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) ) ).

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

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

fof(thm_2Efinite__map_2Ef__o__f__FEMPTY__2,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o__f_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2EFEMPTY_2E0) ).

fof(thm_2Efinite__map_2Ef__o__f__FEMPTY__1,axiom,
    ! [A_27a,A_27b,A_27c,V0f_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Ef__o__f_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2EFEMPTY_2E0) ).

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

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

fof(thm_2Efinite__map_2EFEVERY__FEMPTY,axiom,
    ! [A_27a,A_27b,V0P_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V0P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFEMPTY_2E0)))) ).

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

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

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

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

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

fof(thm_2Efinite__map_2EFLOOKUP__SUBMAP,axiom,
    ! [A_27a,A_27b,V0v_2E0,V1k_2E0,V2g_2E0,V3f_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0))))
        & s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V3f_2E0),s(A_27a,V1k_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0v_2E0))) )
     => s(tyop_2Eoption_2Eoption(A_27b),c_2Efinite__map_2EFLOOKUP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2g_2E0),s(A_27a,V1k_2E0))) = s(tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E1(s(A_27b,V0v_2E0))) ) ).

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

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

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

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

fof(thm_2Efinite__map_2EFMERGE__ASSOC,axiom,
    ! [A_27a,A_27b,V0m_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFMERGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V0m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2EASSOC_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V0m_2E0))) ).

fof(thm_2Efinite__map_2EFMERGE__COMM,axiom,
    ! [A_27a,A_27b,V0m_2E0] : s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Efinite__map_2Efmap(A_27a,A_27b),tyop_2Efinite__map_2Efmap(A_27a,A_27b))),c_2Efinite__map_2EFMERGE_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V0m_2E0))))) = s(tyop_2Emin_2Ebool,c_2Ecombin_2ECOMM_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V0m_2E0))) ).

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

fof(thm_2Efinite__map_2EFUNION__FMERGE,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2m_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))))))
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFMERGE_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),V2m_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0))) ) ).

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

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

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

fof(thm_2Efinite__map_2EFUNION__IDEMPOT,axiom,
    ! [A_27a,A_27b,V0fm_2E0] : s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm_2E0) ).

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

fof(thm_2Efinite__map_2EDRESTRICT__EQ__FUNION,axiom,
    ! [A_27a,A_27b,V0h_2E0,V1h1_2E0,V2h2_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EDISJOINT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1h1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h2_2E0))))))
        & s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1h1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h2_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0h_2E0) )
     => s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V2h2_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0h_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2ECOMPL_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Efinite__map_2EFDOM_2E1(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1h1_2E0))))))) ) ).

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

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

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

fof(thm_2Efinite__map_2ESUBMAP__FUNION__ABSORPTION,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))))
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0))) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1g_2E0) ) ).

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

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

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

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

fof(thm_2Efinite__map_2EMAP__KEYS__BIJ__LINV,axiom,
    ! [A_27a,V0t_2E0,V1f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))
     => s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Epred__set_2ELINV_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V1f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),V0t_2E0))))) = s(tyop_2Efinite__map_2Efmap(tyop_2Enum_2Enum,A_27a),V0t_2E0) ) ).

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

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

fof(thm_2Efinite__map_2EDRESTRICT__MAP__KEYS__IMAGE,axiom,
    ! [A_27a,A_27b,A_27c,V0s_2E0,V1fm_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EINJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))
     => s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1fm_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EIMAGE_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2EDRESTRICT_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1fm_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0))))) ) ).

fof(thm_2Efinite__map_2EDOMSUB__MAP__KEYS,axiom,
    ! [A_27a,A_27b,A_27c,V0s_2E0,V1fm_2E0,V2f_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))))
     => s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1fm_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V0s_2E0))))) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27c),c_2Efinite__map_2EMAP__KEYS_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),c_2Efinite__map_2Efdomsub_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27c),V1fm_2E0),s(A_27a,V0s_2E0))))) ) ).

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

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

fof(thm_2Efinite__map_2Efmap__rel__FEMPTY,axiom,
    ! [A_27a,A_27b,A_27c,V0R_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),c_2Efinite__map_2EFEMPTY_2E0)))) ).

fof(thm_2Efinite__map_2Efmap__rel__FEMPTY2,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1R_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFEMPTY_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f_2E0))))
      <=> s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFEMPTY_2E0) )
      & ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFEMPTY_2E0))))
      <=> s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0f_2E0) = s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),c_2Efinite__map_2EFEMPTY_2E0) ) ) ).

fof(thm_2Efinite__map_2Efmap__rel__refl,axiom,
    ! [A_27a,A_27b,V0x_2E0,V1R_2E0] :
      ( ! [V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0x_2E0),s(tyop_2Efinite__map_2Efmap(A_27b,A_27a),V0x_2E0)))) ) ).

fof(thm_2Efinite__map_2Efmap__rel__FUNION__rels,axiom,
    ! [A_27a,A_27b,A_27c,V0f4_2E0,V1f3_2E0,V2f2_2E0,V3f1_2E0,V4R_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V3f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V2f2_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V1f3_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V0f4_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V4R_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V3f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V1f3_2E0))),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),c_2Efinite__map_2EFUNION_2E2(s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V2f2_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V0f4_2E0)))))) ) ).

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

fof(thm_2Efinite__map_2Efmap__rel__mono,axiom,
    ! [A_27a,A_27b,A_27c,V0f2_2E0,V1f1_2E0,V2R2_2E0,V3R1_2E0] :
      ( ! [V4x_2E0,V5y_2E0] :
          ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0))))
         => p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(A_27a,V4x_2E0))),s(A_27b,V5y_2E0)))) )
     => ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V1f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V0f2_2E0))))
       => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__rel_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V2R2_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27a),V1f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27c,A_27b),V0f2_2E0)))) ) ) ).

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

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

fof(thm_2Efinite__map_2Efmap__EQ__UPTO______EMPTY,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__EQ__UPTO_2E3(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Epred__set_2EEMPTY_2E0))))
    <=> s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0) = s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0) ) ).

fof(thm_2Efinite__map_2Efmap__EQ__UPTO______EQ,axiom,
    ! [A_27a,A_27b,V0vs_2E0,V1f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__EQ__UPTO_2E3(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0vs_2E0)))) ).

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

fof(thm_2Efinite__map_2Efmap__EQ__UPTO______FUPDATE__BOTH______NO__DELETE,axiom,
    ! [A_27a,A_27b,V0f1_2E0,V1f2_2E0,V2ks_2E0,V3k_2E0,V4v_2E0] :
      ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__EQ__UPTO_2E3(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ks_2E0))))
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2Efmap__EQ__UPTO_2E3(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0f1_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3k_2E0),s(A_27b,V4v_2E0))))),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),c_2Efinite__map_2EFUPDATE_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1f2_2E0),s(tyop_2Epair_2Eprod(A_27a,A_27b),c_2Epair_2E_2C_2E2(s(A_27a,V3k_2E0),s(A_27b,V4v_2E0))))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2ks_2E0)))) ) ).

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

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

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

fof(thm_2Efinite__map_2EFEVERY__SUBMAP,axiom,
    ! [A_27a,A_27b,V0fm0_2E0,V1fm_2E0,V2P_2E0] :
      ( ( p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0))))
        & p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2ESUBMAP_2E2(s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm0_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V1fm_2E0)))) )
     => p(s(tyop_2Emin_2Ebool,c_2Efinite__map_2EFEVERY_2E2(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),tyop_2Emin_2Ebool),V2P_2E0),s(tyop_2Efinite__map_2Efmap(A_27a,A_27b),V0fm0_2E0)))) ) ).

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

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

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

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

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

fof(reserved_2Eho_2Eeq__ext,axiom,
    ! [A_27a,A_27b,V0f_2E0,V1g_2E0] :
      ( ! [V2x_2E0] : 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) ) ).

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