%------------------------------------------------------------------------------
% File     : ITP050_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    : quotient.ax [Gau19]
%          : HL4050_4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  300 (  98 unt;  99 typ;   0 def)
%            Number of atoms       :  503 ( 154 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :  307 (   5   ~;   5   |;  61   &)
%                                         (  33 <=>; 203  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   28 (   8 avg)
%            Maximal term depth    :   17 (   2 avg)
%            Number of types       :    7 (   6 usr)
%            Number of type conns  :   92 (  50   >;  42   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   1 usr;   0 prp; 1-2 aty)
%            Number of functors    :   92 (  92 usr;  43 con; 0-4 aty)
%            Number of variables   : 1178 (1176   !;   2   ?;1178   :)
% SPC      : TF0_SAT_EQU_NAR

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

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

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

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

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

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

tff(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

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

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

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

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

tff(combin_i_2E0,type,
    combin_i_2E0: u ).

tff(combin_k_2E0,type,
    combin_k_2E0: u ).

tff(combin_s_2E0,type,
    combin_s_2E0: u ).

tff(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

tff(c_2Equotient_2E_2D_2D_3E_2E0,type,
    c_2Equotient_2E_2D_2D_3E_2E0: u ).

tff(c_2Equotient_2E_2D_2D_3E_2E2,type,
    c_2Equotient_2E_2D_2D_3E_2E2: ( du * du ) > u ).

tff(c_2Equotient_2E_2D_2D_3E_2E3,type,
    c_2Equotient_2E_2D_2D_3E_2E3: ( du * du * du ) > u ).

tff(c_2Equotient_2E_2D_2D_3E_2E4,type,
    c_2Equotient_2E_2D_2D_3E_2E4: ( du * du * du * du ) > u ).

tff(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

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

tff(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

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

tff(c_2Equotient_2E_3D_3D_3D_3E_2E0,type,
    c_2Equotient_2E_3D_3D_3D_3E_2E0: u ).

tff(c_2Equotient_2E_3D_3D_3D_3E_2E2,type,
    c_2Equotient_2E_3D_3D_3D_3E_2E2: ( du * du ) > u ).

tff(c_2Equotient_2E_3D_3D_3D_3E_2E4,type,
    c_2Equotient_2E_3D_3D_3D_3E_2E4: ( du * du * du * du ) > u ).

tff(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

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

tff(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

tff(c_2Ebool_2E_3F_21_2E0,type,
    c_2Ebool_2E_3F_21_2E0: u ).

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

tff(c_2Equotient_2E_3F_21_21_2E0,type,
    c_2Equotient_2E_3F_21_21_2E0: u ).

tff(c_2Equotient_2E_3F_21_21_2E1,type,
    c_2Equotient_2E_3F_21_21_2E1: du > u ).

tff(c_2Ecombin_2EC_2E0,type,
    c_2Ecombin_2EC_2E0: u ).

tff(c_2Ecombin_2EC_2E3,type,
    c_2Ecombin_2EC_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2ECOND_2E0,type,
    c_2Ebool_2ECOND_2E0: u ).

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

tff(c_2Equotient_2EEQUIV_2E0,type,
    c_2Equotient_2EEQUIV_2E0: u ).

tff(c_2Equotient_2EEQUIV_2E1,type,
    c_2Equotient_2EEQUIV_2E1: du > u ).

tff(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

tff(c_2Ecombin_2EI_2E0,type,
    c_2Ecombin_2EI_2E0: u ).

tff(c_2Ecombin_2EI_2E1,type,
    c_2Ecombin_2EI_2E1: du > u ).

tff(c_2Ebool_2EIN_2E0,type,
    c_2Ebool_2EIN_2E0: u ).

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

tff(c_2Ecombin_2EK_2E0,type,
    c_2Ecombin_2EK_2E0: u ).

tff(c_2Ecombin_2EK_2E2,type,
    c_2Ecombin_2EK_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ELET_2E0,type,
    c_2Ebool_2ELET_2E0: u ).

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

tff(c_2Equotient_2EPARTIAL__EQUIV_2E0,type,
    c_2Equotient_2EPARTIAL__EQUIV_2E0: u ).

tff(c_2Equotient_2EPARTIAL__EQUIV_2E1,type,
    c_2Equotient_2EPARTIAL__EQUIV_2E1: du > u ).

tff(c_2Equotient_2EQUOTIENT_2E0,type,
    c_2Equotient_2EQUOTIENT_2E0: u ).

tff(c_2Equotient_2EQUOTIENT_2E3,type,
    c_2Equotient_2EQUOTIENT_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2ERES__ABSTRACT_2E0,type,
    c_2Ebool_2ERES__ABSTRACT_2E0: u ).

tff(c_2Ebool_2ERES__ABSTRACT_2E2,type,
    c_2Ebool_2ERES__ABSTRACT_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ERES__ABSTRACT_2E3,type,
    c_2Ebool_2ERES__ABSTRACT_2E3: ( du * du * du ) > u ).

tff(c_2Ebool_2ERES__EXISTS_2E0,type,
    c_2Ebool_2ERES__EXISTS_2E0: u ).

tff(c_2Ebool_2ERES__EXISTS_2E2,type,
    c_2Ebool_2ERES__EXISTS_2E2: ( du * du ) > u ).

tff(c_2Equotient_2ERES__EXISTS__EQUIV_2E0,type,
    c_2Equotient_2ERES__EXISTS__EQUIV_2E0: u ).

tff(c_2Equotient_2ERES__EXISTS__EQUIV_2E2,type,
    c_2Equotient_2ERES__EXISTS__EQUIV_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ERES__EXISTS__UNIQUE_2E0,type,
    c_2Ebool_2ERES__EXISTS__UNIQUE_2E0: u ).

tff(c_2Ebool_2ERES__EXISTS__UNIQUE_2E2,type,
    c_2Ebool_2ERES__EXISTS__UNIQUE_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ERES__FORALL_2E0,type,
    c_2Ebool_2ERES__FORALL_2E0: u ).

tff(c_2Ebool_2ERES__FORALL_2E2,type,
    c_2Ebool_2ERES__FORALL_2E2: ( du * du ) > u ).

tff(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

tff(c_2Ecombin_2EW_2E0,type,
    c_2Ecombin_2EW_2E0: u ).

tff(c_2Ecombin_2EW_2E2,type,
    c_2Ecombin_2EW_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

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

tff(c_2Ebool_2Eliteral__case_2E0,type,
    c_2Ebool_2Eliteral__case_2E0: u ).

tff(c_2Ebool_2Eliteral__case_2E2,type,
    c_2Ebool_2Eliteral__case_2E2: ( du * du ) > u ).

tff(c_2Ecombin_2Eo_2E0,type,
    c_2Ecombin_2Eo_2E0: u ).

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

tff(c_2Equotient_2Erespects_2E0,type,
    c_2Equotient_2Erespects_2E0: u ).

tff(c_2Equotient_2Erespects_2E1,type,
    c_2Equotient_2Erespects_2E1: du > u ).

tff(c_2Equotient_2Erespects_2E2,type,
    c_2Equotient_2Erespects_2E2: ( du * du ) > u ).

tff(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

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

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

tff(mono_2Ec_2Ebool_2E_2F_5C_2E0,type,
    mono_2Ec_2Ebool_2E_2F_5C_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

tff(mono_2Ec_2Emin_2E_3D_3D_3E_2E0,type,
    mono_2Ec_2Emin_2E_3D_3D_3E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Ebool_2EF_2E0,type,
    mono_2Ec_2Ebool_2EF_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool,type,
    mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

tff(mono_2Ec_2Ebool_2ET_2E0,type,
    mono_2Ec_2Ebool_2ET_2E0: mono_2Etyop_2Emin_2Ebool ).

tff(mono_2Ec_2Ebool_2E_5C_2F_2E0,type,
    mono_2Ec_2Ebool_2E_5C_2F_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 ).

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

tff(mono_2Ec_2Ebool_2E_7E_2E0,type,
    mono_2Ec_2Ebool_2E_7E_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool_20mono_2EA_27b_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X1_2E0)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Efun(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_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),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_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(X1_2E0)))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_2D_2D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),X2_2E0),s(A_27a,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(A_27a,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27b),X2_2E0))),s(A_27a,X3_2E0))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_2D_2D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27d_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( s(A_27b,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0),s(A_27a,X3_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),X2_2E0))),s(A_27a,X3_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29_20mono_2EA_27c_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b))))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2EA_27e_20mono_2EA_27d_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27d: d,A_27e: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27d),X0_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27a,A_27b)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),X2_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27e_2CA_27f_29_20mono_2EA_27d_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27d),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X2_2E0))) = s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c))))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27f_20mono_2EA_27e_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27c),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27b_20mono_2EA_27f_20mono_2EA_27e_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))) = s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X0_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27f),X2_2E0))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_2D_2D_3E_2E2_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_2D_2D_3E_2E4_2Emono_2EA_27c_20mono_2EA_27b_20mono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(A_27c,X3_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(A_27c,X3_2E0))) ) ).

tff(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27d_20mono_2EA_27c_20mono_2EA_27a_20mono_2EA_27f,axiom,
    ! [A_27a: d,A_27c: d,A_27d: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(tyop_2Emin_2Efun(A_27d,A_27f),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27d,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27d,A_27f))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27d,A_27f)))),c_2Equotient_2E_2D_2D_3E_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),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_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),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_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),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_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X3_2E0)))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(X1_2E0)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),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))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),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_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(X1_2E0)))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X3_2E0)))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),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_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X3_2E0)))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Ebool),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_27c)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),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_27c)),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_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),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_27c)),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X3_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2E_3D_3D_3D_3E_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))) ) ).

tff(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X3_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)))),c_2Equotient_2E_3D_3D_3D_3E_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X2_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X3_2E0)))) ) ).

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

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

tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_21_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Equotient_2E_3F_21_21_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3F_21_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Equotient_2E_3F_21_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0),s(A_27b,X1_2E0),s(A_27a,X2_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(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(A_27b,tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),X0_2E0))),s(A_27b,X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ecombin_2EC_2E3_2Emono_2EA_27d_20mono_2EA_27e_20mono_2EA_27f,axiom,
    ! [A_27d: d,A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27f,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0),s(A_27e,X1_2E0),s(A_27d,X2_2E0))) = s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27f),app_2E2(s(tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27d,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),tyop_2Emin_2Efun(A_27e,tyop_2Emin_2Efun(A_27d,A_27f))),c_2Ecombin_2EC_2E0),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),X0_2E0))),s(A_27e,X1_2E0))),s(A_27d,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_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,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27a,X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: mono_2Etyop_2Emin_2Ebool,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_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,i_mono_2Etyop_2Emin_2Ebool(X0_2E0)))),s(A_27b,X1_2E0))),s(A_27b,X2_2E0))) ) ).

tff(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Equotient_2EEQUIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,X0_2E0))) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(A_27a,X0_2E0))) ) ).

tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] : ( s(A_27b,c_2Ecombin_2EI_2E1(s(A_27b,X0_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0),s(A_27b,X0_2E0))) ) ).

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

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

tff(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(A_27a,c_2Ecombin_2EK_2E2(s(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(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),c_2Ecombin_2EK_2E0),s(A_27a,X0_2E0))),s(A_27b,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2EK_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(A_27c,c_2Ecombin_2EK_2E2(s(A_27c,X0_2E0),s(A_27d,X1_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27d,A_27c)),c_2Ecombin_2EK_2E0),s(A_27c,X0_2E0))),s(A_27d,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(A_27c,X1_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ebool_2ELET_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(A_27c,X1_2E0))) ) ).

tff(arityeq1_2Ec_2Equotient_2EPARTIAL__EQUIV_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EPARTIAL__EQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),c_2Equotient_2EPARTIAL__EQUIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,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_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27d,axiom,
    ! [A_27a: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,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_2Emin_2Efun(A_27a,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27a),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27a),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27d),X1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27e,axiom,
    ! [A_27b: d,A_27e: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),X1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27b),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27e),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27b),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27e),X1_2E0))),s(tyop_2Emin_2Efun(A_27e,A_27b),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27c_20mono_2EA_27f,axiom,
    ! [A_27c: d,A_27f: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27f,A_27c),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27f),X1_2E0))),s(tyop_2Emin_2Efun(A_27f,A_27c),X2_2E0)))) ) ).

tff(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28A_27c_2CA_27d_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Ebool))),c_2Equotient_2EQUOTIENT_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),X2_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__ABSTRACT_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq3_2Ec_2Ebool_2ERES__ABSTRACT_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] : ( s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0),s(A_27a,X2_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b))),c_2Ebool_2ERES__ABSTRACT_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))),s(A_27a,X2_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__EXISTS_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2ERES__EXISTS__EQUIV_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Equotient_2ERES__EXISTS__EQUIV_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__EXISTS__UNIQUE_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__EXISTS__UNIQUE_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ebool_2ERES__FORALL_2E2_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),c_2Ebool_2ERES__FORALL_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2EW_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(A_27d,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0),s(A_27c,X1_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ecombin_2EW_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),X0_2E0))),s(A_27c,X1_2E0))) ) ).

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

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(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_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(A_27a,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ebool_2Eliteral__case_2E2_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] : ( s(A_27d,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0),s(A_27c,X1_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Ebool_2Eliteral__case_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),X0_2E0))),s(A_27c,X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) = 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_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0))) ) ).

tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27d_20mono_2EA_27f_20mono_2EA_27e,axiom,
    ! [A_27d: d,A_27e: d,A_27f: d,X0_2E0: u,X1_2E0: u] : ( s(tyop_2Emin_2Efun(A_27d,A_27f),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),X0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),X1_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27f),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27e),tyop_2Emin_2Efun(A_27d,A_27f))),c_2Ecombin_2Eo_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),X0_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27e),X1_2E0))) ) ).

tff(arityeq1_2Ec_2Equotient_2Erespects_2E1_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u] : ( s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,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_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))) ) ).

tff(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2EA_27a_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0),s(A_27a,X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),X0_2E0))),s(A_27a,X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27b_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2CA_27c_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27a: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0)))) ) ).

tff(arityeq2_2Ec_2Equotient_2Erespects_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27b_2CA_27c_29_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),X0_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2Erespects_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0)))) ) ).

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

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

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

tff(monoeq_2Emono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0) ).

tff(monoeq_2Emono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
    s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)) = s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ecombin_2EI_2E0) ).

tff(thm_2Equotient_2EEQUIV__def,axiom,
    ! [A_27a: d,V0E_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0)))))
    <=> ! [V1x_2E0: u,V2y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0E_2E0),s(A_27a,V1x_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)),V0E_2E0),s(A_27a,V2y_2E0))) ) ) ) ).

tff(thm_2Equotient_2EPARTIAL__EQUIV__def,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EPARTIAL__EQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
    <=> ( ? [V1x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),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,V1x_2E0)))))
        & ! [V2x_2E0: u,V3y_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V3y_2E0)))))
          <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V2x_2E0))),s(A_27a,V2x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3y_2E0))),s(A_27a,V3y_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)),V0R_2E0),s(A_27a,V2x_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)),V0R_2E0),s(A_27a,V3y_2E0))) ) ) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__def,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
    <=> ( ! [V3a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3a_2E0))))) = s(A_27b,V3a_2E0) )
        & ! [V4a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4a_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4a_2E0)))))))
        & ! [V5r_2E0: u,V6s_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5r_2E0))),s(A_27a,V6s_2E0)))))
          <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5r_2E0))),s(A_27a,V5r_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6s_2E0))),s(A_27a,V6s_2E0)))))
              & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V5r_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V6s_2E0))) ) ) ) ) ) ).

tff(thm_2Equotient_2EFUN__MAP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u,V3x_27_2E0: u] : ( s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2x_2E0),s(A_27a,V3x_27_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2x_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V3x_27_2E0))))))) ) ).

tff(thm_2Equotient_2EFUN__REL,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_2E0: u,V2f_2E0: u,V3g_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0)))))
    <=> ! [V4x_2E0: u,V5y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3g_2E0),s(A_27a,V5y_2E0))))))) ) ) ).

tff(thm_2Equotient_2Erespects__def,axiom,
    ! [A_27a: d,A_27b: d] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2Erespects_2E0) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EW_2E0) ) ).

tff(thm_2Equotient_2E_3F_21_21,axiom,
    ! [A_27a: d,V0P_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3F_21_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))) ) ).

tff(thm_2Equotient_2ERES__EXISTS__EQUIV__DEF,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V1x_27_2E0: u,V3x_2E0: u,V0x_2E0: u,V4y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))),s(A_27a,V4y_2E0)))))
        <=> ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V3x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V4y_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))))) ) )
     => ( ! [V0x_2E0: u,V1x_27_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_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_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))),s(tyop_2Emin_2Efun(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(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0)))))) )
       => ( ! [V1x_27_2E0: u,V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))),s(A_27a,V2x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0),s(A_27a,V2x_2E0)))) )
         => ! [V0x_2E0: u,V1x_27_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))
            <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0)))))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_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_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1x_27_2E0))))))) ) ) ) ) ) ).

tff(thm_2Equotient_2EFUN__REL__EQUALS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0))))) )
             => ( ( s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0))) )
              <=> ! [V8x_2E0: u,V9y_2E0: u] :
                    ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0)))))
                   => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ) ) ).

tff(thm_2Equotient_2EEQUIV__IMP__PARTIAL__EQUIV,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EPARTIAL__EQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))))) ) ).

tff(thm_2Equotient_2EQUOTIENT__ABS__REP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3a_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3a_2E0))))) = s(A_27b,V3a_2E0) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__REP__REFL,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3a_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3a_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3a_2E0))))))) ) ).

tff(thm_2Equotient_2EQUOTIENT__REL,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3r_2E0: u,V4s_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V4s_2E0)))))
        <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V3r_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4s_2E0))),s(A_27a,V4s_2E0)))))
            & ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V3r_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V4s_2E0))) ) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__REL__ABS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3r_2E0: u,V4s_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V4s_2E0)))))
         => ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V3r_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V4s_2E0))) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__REL__ABS__EQ,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3r_2E0: u,V4s_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V3r_2E0)))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4s_2E0))),s(A_27a,V4s_2E0)))))
           => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V4s_2E0)))))
            <=> ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V3r_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V4s_2E0))) ) ) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__REL__REP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3a_2E0: u,V4b_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3a_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4b_2E0)))))))
        <=> ( s(A_27b,V3a_2E0) = s(A_27b,V4b_2E0) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__REP__ABS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3r_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3r_2E0))),s(A_27a,V3r_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V3r_2E0))))))),s(A_27a,V3r_2E0))))) ) ) ).

tff(thm_2Equotient_2EIDENTITY__EQUIV,axiom,
    ! [A_27a: d] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0))))) ).

tff(thm_2Equotient_2EIDENTITY__QUOTIENT,axiom,
    ! [A_27a: d] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0))))) ).

tff(thm_2Equotient_2EEQUIV__REFL__SYM__TRANS,axiom,
    ! [A_27a: d,V0R_2E0: u] :
      ( ! [V1x_2E0: u,V2y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V2y_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)),V0R_2E0),s(A_27a,V1x_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)),V0R_2E0),s(A_27a,V2y_2E0))) ) )
    <=> ( ! [V3x_2E0: u] : p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V3x_2E0)))))
        & ! [V4x_2E0: u,V5y_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y_2E0))),s(A_27a,V4x_2E0))))) )
        & ! [V6x_2E0: u,V7y_2E0: u,V8z_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0))),s(A_27a,V7y_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7y_2E0))),s(A_27a,V8z_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V6x_2E0))),s(A_27a,V8z_2E0))))) ) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__SYM,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3x_2E0: u,V4y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V3x_2E0))))) ) ) ).

tff(thm_2Equotient_2EQUOTIENT__TRANS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3x_2E0: u,V4y_2E0: u,V5z_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4y_2E0))),s(A_27a,V5z_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V5z_2E0))))) ) ) ).

tff(thm_2Equotient_2EFUN__MAP__THM,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2h_2E0: u,V3x_2E0: u] : ( s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(tyop_2Emin_2Efun(A_27c,A_27b),V2h_2E0),s(A_27a,V3x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V1g_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27b),V2h_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V0f_2E0),s(A_27a,V3x_2E0))))))) ) ).

tff(thm_2Equotient_2EFUN__MAP__I,axiom,
    ! [A_27a: d,A_27b: d] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),c_2Ecombin_2EI_2E0),s(tyop_2Emin_2Efun(A_27b,A_27b),c_2Ecombin_2EI_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Ecombin_2EI_2E0) ) ).

tff(thm_2Equotient_2EIN__FUN,axiom,
    ! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,V2s_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V3x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(V1g_2E0)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0)))))) = mono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool(V1g_2E0,j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V2s_2E0))))) ) ).

tff(thm_2Equotient_2EFUN__REL__EQ,axiom,
    ! [A_27a: d,A_27b: d] : ( s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0))) = s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0) ) ).

tff(thm_2Equotient_2EFUN__QUOTIENT,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27c,A_27d)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0))),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))))))) ) ) ).

tff(thm_2Equotient_2ERESPECTS,axiom,
    ! [A_27a: d,V0R_2E0: u,V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))) ) ).

tff(thm_2Equotient_2EIN__RESPECTS,axiom,
    ! [A_27a: d,V0R_2E0: u,V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V1x_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V1x_2E0))),s(A_27a,V1x_2E0)))) ) ).

tff(thm_2Equotient_2ERESPECTS__THM,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_2E0: u,V2f_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))))
    <=> ! [V3x_2E0: u,V4y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))))))) ) ) ).

tff(thm_2Equotient_2ERESPECTS__MP,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_2E0: u,V2f_2E0: u,V3x_2E0: u,V4y_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V3x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(A_27a,V4y_2E0))))))) ) ).

tff(thm_2Equotient_2ERESPECTS__REP__ABS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4f_2E0: u,V5x_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V5x_2E0))),s(A_27a,V5x_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(A_27a,V5x_2E0))))))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(A_27a,V5x_2E0))))))) ) ) ).

tff(thm_2Equotient_2ERESPECTS__o,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R1_2E0: u,V1R2_2E0: u,V2R3_2E0: u,V3f_2E0: u,V4g_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V2R3_2E0))),s(tyop_2Emin_2Efun(A_27b,A_27c),V3f_2E0)))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V2R3_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4g_2E0))))))) ) ).

tff(thm_2Equotient_2ERES__EXISTS__EQUIV,axiom,
    ! [A_27a: d,F2_2E0: u,F1_2E0: u,F0_2E0: u] :
      ( ! [V1m_2E0: u,V3x_2E0: u,V0R_2E0: u,V4y_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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_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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(A_27a,V4y_2E0)))))
        <=> ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V3x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V4y_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x_2E0))),s(A_27a,V4y_2E0))))) ) )
     => ( ! [V0R_2E0: u,V1m_2E0: u,V3x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_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_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V3x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(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(A_27a,tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,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(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)))),F2_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V3x_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0)))))) )
       => ( ! [V1m_2E0: u,V2x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))),s(A_27a,V2x_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0),s(A_27a,V2x_2E0)))) )
         => ! [V0R_2E0: u,V1m_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0)))))
            <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_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)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0)))))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_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_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))),F1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1m_2E0))))))) ) ) ) ) ) ).

tff(thm_2Equotient_2EFUN__REL__EQ__REL,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
            <=> ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & ( s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0))) ) ) ) ) ) ).

tff(thm_2Equotient_2EFUN__REL__MP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u,V8x_2E0: u,V9y_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EFUN__REL__IMP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & ( s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0))) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0))) ) )
             => ! [V8x_2E0: u,V9y_2E0: u] :
                  ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0)))))
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2EEQUALS__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3x_2E0: u,V4y_2E0: u] :
          ( ( s(A_27b,V3x_2E0) = s(A_27b,V4y_2E0) )
        <=> p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3x_2E0))))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4y_2E0))))))) ) ) ).

tff(thm_2Equotient_2EEQUALS__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3x1_2E0: u,V4x2_2E0: u,V5y1_2E0: u,V6y2_2E0: u] :
          ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x1_2E0))),s(A_27a,V4x2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5y1_2E0))),s(A_27a,V6y2_2E0))))) )
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3x1_2E0))),s(A_27a,V5y1_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V4x2_2E0))),s(A_27a,V6y2_2E0)))) ) ) ) ).

tff(thm_2Equotient_2ELAMBDA__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V5rep2_2E0: u,V6f_2E0: u,V1abs1_2E0: u,V8x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0))),s(A_27a,V8x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(A_27a,V8x_2E0))))))) )
     => ! [V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
         => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
             => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0))),s(A_27c,V7x_2E0))) ) ) ) ) ).

tff(thm_2Equotient_2ELAMBDA__PRS1,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V1abs1_2E0: u,V5rep2_2E0: u,V6f_2E0: u,V8x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(A_27a,V8x_2E0))) = s(A_27b,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27a,V8x_2E0))) )
     => ! [V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
         => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
             => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b))),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27d,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)))),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0))),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(A_27c,V7x_2E0))) ) ) ) ) ).

tff(thm_2Equotient_2ELAMBDA__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,F0_2E0: u] :
      ( ! [V6f1_2E0: u,V8x_2E0: u] : ( s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0))),s(A_27a,V8x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(A_27a,V8x_2E0))) )
     => ! [V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
         => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
             => ! [V6f1_2E0: u,V7f2_2E0: u] :
                  ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0)))))
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),F0_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2EABSTRACT__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u] : ( s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0) = s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2ERES__ABSTRACT__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f1_2E0: u,V7f2_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0)))))
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2ELET__RES__ABSTRACT,axiom,
    ! [A_27a: d,A_27b: d,V0r_2E0: u,V1lam_2E0: u,V2v_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2EIN_2E2(s(A_27a,V2v_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0)))))
     => ( s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0r_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1lam_2E0))),s(A_27a,V2v_2E0))) = s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1lam_2E0),s(A_27a,V2v_2E0))) ) ) ).

tff(thm_2Equotient_2ELAMBDA__REP__ABS__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0REL1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u,V3REL2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u,V6f1_2E0: u,V7f2_2E0: u] :
      ( ( ! [V8r_2E0: u,V9r_27_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL1_2E0),s(A_27a,V8r_2E0))),s(A_27a,V9r_27_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL1_2E0),s(A_27a,V8r_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(A_27a,V9r_27_2E0))))))))) )
        & ! [V10r_2E0: u,V11r_27_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3REL2_2E0),s(A_27b,V10r_2E0))),s(A_27b,V11r_27_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3REL2_2E0),s(A_27b,V10r_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(A_27b,V11r_27_2E0))))))))) )
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3REL2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3REL2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7f2_2E0))))))))) ) ).

tff(thm_2Equotient_2EREP__ABS__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0REL_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3x1_2E0: u,V4x2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL_2E0),s(A_27a,V3x1_2E0))),s(A_27a,V4x2_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0REL_2E0),s(A_27a,V3x1_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,V4x2_2E0))))))))) ) ) ).

tff(thm_2Equotient_2EFORALL__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))))) ) ) ).

tff(thm_2Equotient_2ERES__FORALL__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u,V4g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))))
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))) ) ) ) ).

tff(thm_2Equotient_2ERES__FORALL__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3P_2E0: u,V4f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4f_2E0)))))) ) ) ).

tff(thm_2Equotient_2EEXISTS__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))))) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u,V4g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))))
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))) ) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3P_2E0: u,V4f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3P_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V4f_2E0)))))) ) ) ).

tff(thm_2Equotient_2EEXISTS__UNIQUE__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29(mono_2Ec_2Ecombin_2EI_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V3f_2E0)))))) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__EQUIV__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3f_2E0: u,V4g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))))
         => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3f_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4g_2E0)))) ) ) ) ).

tff(thm_2Equotient_2ECOND__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3a_2E0: mono_2Etyop_2Emin_2Ebool,V4b_2E0: u,V5c_2E0: u] : ( s(A_27b,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V3a_2E0)),s(A_27b,V4b_2E0),s(A_27b,V5c_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V3a_2E0)),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V4b_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V5c_2E0))))))) ) ) ).

tff(thm_2Equotient_2ECOND__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3a1_2E0: mono_2Etyop_2Emin_2Ebool,V4a2_2E0: mono_2Etyop_2Emin_2Ebool,V5b1_2E0: u,V6b2_2E0: u,V7c1_2E0: u,V8c2_2E0: u] :
          ( ( ( V3a1_2E0 = V4a2_2E0 )
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V5b1_2E0))),s(A_27a,V6b2_2E0)))))
            & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V7c1_2E0))),s(A_27a,V8c2_2E0))))) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V3a1_2E0)),s(A_27a,V5b1_2E0),s(A_27a,V7c1_2E0))))),s(A_27a,c_2Ebool_2ECOND_2E3(s(tyop_2Emin_2Ebool,i_mono_2Etyop_2Emin_2Ebool(V4a2_2E0)),s(A_27a,V6b2_2E0),s(A_27a,V8c2_2E0))))))) ) ) ).

tff(thm_2Equotient_2ELET__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,V7x_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2ELET__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u,V8x_2E0: u,V9y_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,c_2Ebool_2ELET_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2Eliteral__case__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,V7x_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2Eliteral__case__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u,V8x_2E0: u,V9y_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,c_2Ebool_2Eliteral__case_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EAPPLY__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(A_27b,c_2Equotient_2E_2D_2D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27c,A_27d),V6f_2E0),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,V7x_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EAPPLY__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7g_2E0: u,V8x_2E0: u,V9y_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x_2E0))),s(A_27a,V9y_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V6f_2E0),s(A_27a,V8x_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V7g_2E0),s(A_27a,V9y_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EI__PRS,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3e_2E0: u] : ( s(A_27b,c_2Ecombin_2EI_2E1(s(A_27b,V3e_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0),s(A_27b,V3e_2E0))))))) ) ) ).

tff(thm_2Equotient_2EI__RSP,axiom,
    ! [A_27a: d,A_27b: d,V0R_2E0: u,V1abs_2E0: u,V2rep_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V1abs_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),V2rep_2E0)))))
     => ! [V3e1_2E0: u,V4e2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,V3e1_2E0))),s(A_27a,V4e2_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V3e1_2E0))))),s(A_27a,c_2Ecombin_2EI_2E1(s(A_27a,V4e2_2E0))))))) ) ) ).

tff(thm_2Equotient_2EK__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6x_2E0: u,V7y_2E0: u] : ( s(A_27c,c_2Ecombin_2EK_2E2(s(A_27c,V6x_2E0),s(A_27d,V7y_2E0))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,V6x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0),s(A_27d,V7y_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EK__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6x1_2E0: u,V7x2_2E0: u,V8y1_2E0: u,V9y2_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V6x1_2E0))),s(A_27a,V7x2_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,V8y1_2E0))),s(A_27b,V9y2_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V6x1_2E0),s(A_27b,V8y1_2E0))))),s(A_27a,c_2Ecombin_2EK_2E2(s(A_27a,V7x2_2E0),s(A_27b,V9y2_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2Eo__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0)))))
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0)))))
             => ! [V9f_2E0: u,V10g_2E0: u] : ( s(tyop_2Emin_2Efun(A_27d,A_27f),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27e,A_27f),V9f_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V10g_2E0))) = s(tyop_2Emin_2Efun(A_27d,A_27f),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0),s(tyop_2Emin_2Efun(A_27e,A_27f),V9f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27e),V10g_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2Eo__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0)))))
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0)))))
             => ! [V9f1_2E0: u,V10f2_2E0: u,V11g1_2E0: u,V12g2_2E0: u] :
                  ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V9f1_2E0),s(tyop_2Emin_2Efun(A_27b,A_27c),V10f2_2E0)))))
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V11g1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V12g2_2E0))))) )
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V9f1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V11g1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27c),c_2Ecombin_2Eo_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),V10f2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V12g2_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2EC__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0)))))
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0)))))
             => ! [V9f_2E0: u,V10x_2E0: u,V11y_2E0: u] : ( s(A_27f,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V9f_2E0),s(A_27e,V10x_2E0),s(A_27d,V11y_2E0))) = s(A_27f,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27e,A_27f),tyop_2Emin_2Efun(A_27b,A_27c)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0))),s(tyop_2Emin_2Efun(A_27d,tyop_2Emin_2Efun(A_27e,A_27f)),V9f_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0),s(A_27e,V10x_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0),s(A_27d,V11y_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2EC__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27d),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27e),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27e,A_27b),V5rep2_2E0)))))
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_2E0: u] :
              ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(tyop_2Emin_2Efun(A_27c,A_27f),V7abs3_2E0),s(tyop_2Emin_2Efun(A_27f,A_27c),V8rep3_2E0)))))
             => ! [V9f1_2E0: u,V10f2_2E0: u,V11x1_2E0: u,V12x2_2E0: u,V13y1_2E0: u,V14y2_2E0: u] :
                  ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V9f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V10f2_2E0)))))
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,V11x1_2E0))),s(A_27b,V12x2_2E0)))))
                    & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V13y1_2E0))),s(A_27a,V14y2_2E0))))) )
                 => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Ebool)),V6R3_2E0),s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V9f1_2E0),s(A_27b,V11x1_2E0),s(A_27a,V13y1_2E0))))),s(A_27c,c_2Ecombin_2EC_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V10f2_2E0),s(A_27b,V12x2_2E0),s(A_27a,V14y2_2E0))))))) ) ) ) ) ).

tff(thm_2Equotient_2EW__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f_2E0: u,V7x_2E0: u] : ( s(A_27d,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),V6f_2E0),s(A_27c,V7x_2E0))) = s(A_27d,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E3(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27d),tyop_2Emin_2Efun(A_27a,A_27b)),c_2Equotient_2E_2D_2D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0))),s(tyop_2Emin_2Efun(A_27c,tyop_2Emin_2Efun(A_27c,A_27d)),V6f_2E0))),s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0),s(A_27c,V7x_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EW__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27b,A_27d),V4abs2_2E0),s(tyop_2Emin_2Efun(A_27d,A_27b),V5rep2_2E0)))))
         => ! [V6f1_2E0: u,V7f2_2E0: u,V8x1_2E0: u,V9x2_2E0: u] :
              ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Ebool)),c_2Equotient_2E_3D_3D_3D_3E_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V6f1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V7f2_2E0)))))
                & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V8x1_2E0))),s(A_27a,V9x2_2E0))))) )
             => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V6f1_2E0),s(A_27a,V8x1_2E0))))),s(A_27b,c_2Ecombin_2EW_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27b)),V7f2_2E0),s(A_27a,V9x2_2E0))))))) ) ) ) ).

tff(thm_2Equotient_2EEQ__IMPLIES,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1Q_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( V0P_2E0 = V1Q_2E0 )
     => ( p(V0P_2E0)
       => p(V1Q_2E0) ) ) ).

tff(thm_2Equotient_2EEQUALS__IMPLIES,axiom,
    ! [A_27a: d,V0P_2E0: u,V1P_27_2E0: u,V2Q_2E0: u,V3Q_27_2E0: u] :
      ( ( ( s(A_27a,V0P_2E0) = s(A_27a,V2Q_2E0) )
        & ( s(A_27a,V1P_27_2E0) = s(A_27a,V3Q_27_2E0) ) )
     => ( ( s(A_27a,V0P_2E0) = s(A_27a,V1P_27_2E0) )
       => ( s(A_27a,V2Q_2E0) = s(A_27a,V3Q_27_2E0) ) ) ) ).

tff(thm_2Equotient_2ECONJ__IMPLIES,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1P_27_2E0: mono_2Etyop_2Emin_2Ebool,V2Q_2E0: mono_2Etyop_2Emin_2Ebool,V3Q_27_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(V0P_2E0)
         => p(V2Q_2E0) )
        & ( p(V1P_27_2E0)
         => p(V3Q_27_2E0) ) )
     => ( ( p(V0P_2E0)
          & p(V1P_27_2E0) )
       => ( p(V2Q_2E0)
          & p(V3Q_27_2E0) ) ) ) ).

tff(thm_2Equotient_2EDISJ__IMPLIES,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1P_27_2E0: mono_2Etyop_2Emin_2Ebool,V2Q_2E0: mono_2Etyop_2Emin_2Ebool,V3Q_27_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(V0P_2E0)
         => p(V2Q_2E0) )
        & ( p(V1P_27_2E0)
         => p(V3Q_27_2E0) ) )
     => ( ( p(V0P_2E0)
          | p(V1P_27_2E0) )
       => ( p(V2Q_2E0)
          | p(V3Q_27_2E0) ) ) ) ).

tff(thm_2Equotient_2EIMP__IMPLIES,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1P_27_2E0: mono_2Etyop_2Emin_2Ebool,V2Q_2E0: mono_2Etyop_2Emin_2Ebool,V3Q_27_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( ( p(V2Q_2E0)
         => p(V0P_2E0) )
        & ( p(V1P_27_2E0)
         => p(V3Q_27_2E0) ) )
     => ( ( p(V0P_2E0)
         => p(V1P_27_2E0) )
       => ( p(V2Q_2E0)
         => p(V3Q_27_2E0) ) ) ) ).

tff(thm_2Equotient_2ENOT__IMPLIES,axiom,
    ! [V0P_2E0: mono_2Etyop_2Emin_2Ebool,V1Q_2E0: mono_2Etyop_2Emin_2Ebool] :
      ( ( p(V1Q_2E0)
       => p(V0P_2E0) )
     => ( ~ p(V0P_2E0)
       => ~ p(V1Q_2E0) ) ) ).

tff(thm_2Equotient_2EEQUALS__EQUIV__IMPLIES,axiom,
    ! [A_27a: d,V0b2_2E0: u,V1b1_2E0: u,V2a2_2E0: u,V3a1_2E0: u,V4R_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0)))))
     => ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V3a1_2E0))),s(A_27a,V2a2_2E0)))))
          & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V1b1_2E0))),s(A_27a,V0b2_2E0))))) )
       => ( ( s(A_27a,V3a1_2E0) = s(A_27a,V1b1_2E0) )
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V4R_2E0),s(A_27a,V2a2_2E0))),s(A_27a,V0b2_2E0))))) ) ) ) ).

tff(thm_2Equotient_2EABSTRACT__RES__ABSTRACT,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4f_2E0: u,V5g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5g_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V5g_2E0))))))) ) ) ).

tff(thm_2Equotient_2ERES__ABSTRACT__ABSTRACT,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EQUOTIENT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27a,A_27c),V1abs1_2E0),s(tyop_2Emin_2Efun(A_27c,A_27a),V2rep1_2E0)))))
     => ! [V3R2_2E0: u,V4f_2E0: u,V5g_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),V5g_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V3R2_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),c_2Ebool_2ERES__ABSTRACT_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V4f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V5g_2E0))))) ) ) ).

tff(thm_2Equotient_2EEQUIV__RES__ABSTRACT__LEFT,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_2E0: u,V2f1_2E0: u,V3f2_2E0: u,V4x1_2E0: u,V5x2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x1_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V5x2_2E0)))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V4x1_2E0))),s(A_27a,V4x1_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x1_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V5x2_2E0))))))) ) ).

tff(thm_2Equotient_2EEQUIV__RES__ABSTRACT__RIGHT,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_2E0: u,V2f1_2E0: u,V3f2_2E0: u,V4x1_2E0: u,V5x2_2E0: u] :
      ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x1_2E0))))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V5x2_2E0)))))))
        & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0),s(A_27a,V5x2_2E0))),s(A_27a,V5x2_2E0))))) )
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V1R2_2E0),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0),s(A_27a,V4x1_2E0))))),s(A_27b,c_2Ebool_2ERES__ABSTRACT_2E3(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R1_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V3f2_2E0),s(A_27a,V5x2_2E0))))))) ) ).

tff(thm_2Equotient_2EEQUIV__RES__FORALL,axiom,
    ! [A_27a: d,V0E_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0)))))
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) ) ) ).

tff(thm_2Equotient_2EEQUIV__RES__EXISTS,axiom,
    ! [A_27a: d,V0E_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0)))))
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) ) ) ).

tff(thm_2Equotient_2EEQUIV__RES__EXISTS__UNIQUE,axiom,
    ! [A_27a: d,V0E_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2EEQUIV_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0)))))
     => ( j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0E_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) = j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))) ) ) ).

tff(thm_2Equotient_2EFORALL__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) ) ) ).

tff(thm_2Equotient_2EEXISTS__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u] :
      ( ! [V2x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))))
         => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0))))) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ERES__FORALL__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u,V2R_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3x_2E0)))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1Q_2E0: u,V2R_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(A_27a,V3x_2E0)))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ELEFT__RES__FORALL__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1R_2E0: u,V2Q_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(A_27a,V3x_2E0)))))
          & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) ) ) ).

tff(thm_2Equotient_2ERIGHT__RES__FORALL__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1R_2E0: u,V2Q_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(A_27a,V3x_2E0)))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__FORALL_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ELEFT__RES__EXISTS__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1R_2E0: u,V2Q_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(A_27a,V3x_2E0)))))
         => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0))))) ) ) ).

tff(thm_2Equotient_2ERIGHT__RES__EXISTS__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1R_2E0: u,V2Q_2E0: u] :
      ( ! [V3x_2E0: u] :
          ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(A_27a,V3x_2E0)))))
          & ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))) ) ) ).

tff(thm_2Equotient_2EEXISTS__UNIQUE__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1E_2E0: u,V2Q_2E0: u] :
      ( ( ! [V3x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1E_2E0),s(A_27a,V3x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))) ) )
        & ! [V4x_2E0: u,V5y_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1E_2E0),s(A_27a,V4x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1E_2E0),s(A_27a,V5y_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1E_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1E_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__UNIQUE__RESPECTS__REGULAR,axiom,
    ! [A_27a: d,V0R_2E0: u,V1P_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))
     => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0))))) ) ).

tff(thm_2Equotient_2ERES__EXISTS__UNIQUE__REGULAR,axiom,
    ! [A_27a: d,V0P_2E0: u,V1R_2E0: u,V2Q_2E0: u] :
      ( ( ! [V3x_2E0: u] :
            ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))))
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V3x_2E0))))) )
        & ! [V4x_2E0: u,V5y_2E0: u] :
            ( ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V4x_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2Erespects_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V5y_2E0)))))
              & p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0),s(A_27a,V5y_2E0))))) )
           => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(A_27a,V4x_2E0))),s(A_27a,V5y_2E0))))) ) )
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V1R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))) ) ) ).

tff(thm_2Equotient_2ERES__EXISTS__UNIQUE__REGULAR__SAME,axiom,
    ! [A_27a: d,V0R_2E0: u,V1P_2E0: u,V2Q_2E0: u] :
      ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2E_3D_3D_3D_3E_2E4(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29(mono_2Ec_2Emin_2E_3D_2E0_2Emono_2Etyop_2Emin_2Ebool)),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0)))))
     => ( p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Ebool_2ERES__EXISTS__UNIQUE_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Equotient_2Erespects_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0)))))
       => p(j_mono_2Etyop_2Emin_2Ebool(s(tyop_2Emin_2Ebool,c_2Equotient_2ERES__EXISTS__EQUIV_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),V0R_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2Q_2E0))))) ) ) ).

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