%------------------------------------------------------------------------------
% File     : ITP073^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : quotient_sum.ax [Gau19]
%          : HL4073^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  138 (  55 unt;  63 typ;   0 def)
%            Number of atoms       :  184 (  67 equ;   1 cnn)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives : 4782 (   1   ~;   1   |;   8   &;4728   @)
%                                         (   8 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   44 (  10 avg;4728 nst)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   62 (  60 usr;  26 con; 0-4 aty)
%            Number of variables   :  420 (   0   ^ 419   !;   1   ?; 420   :)
% SPC      : TH0_SAT_EQU_NAR

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

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

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

thf(tyop_2Emin_2Ebool,type,
    tyop_2Emin_2Ebool: d ).

thf(tyop_2Emin_2Efun,type,
    tyop_2Emin_2Efun: d > d > d ).

thf(tyop_2Esum_2Esum,type,
    tyop_2Esum_2Esum: d > d > d ).

thf(s,type,
    s: d > u > du ).

thf(app_2E2,type,
    app_2E2: du > du > u ).

thf(combin_i_2E0,type,
    combin_i_2E0: u ).

thf(combin_k_2E0,type,
    combin_k_2E0: u ).

thf(combin_s_2E0,type,
    combin_s_2E0: u ).

thf(c_2Ebool_2E_21_2E0,type,
    c_2Ebool_2E_21_2E0: u ).

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

thf(c_2Esum_2E_2B_2B_2E0,type,
    c_2Esum_2E_2B_2B_2E0: u ).

thf(c_2Esum_2E_2B_2B_2E2,type,
    c_2Esum_2E_2B_2B_2E2: du > du > u ).

thf(c_2Esum_2E_2B_2B_2E3,type,
    c_2Esum_2E_2B_2B_2E3: du > du > du > u ).

thf(c_2Equotient__sum_2E_2B_2B_2B_2E0,type,
    c_2Equotient__sum_2E_2B_2B_2B_2E0: u ).

thf(c_2Equotient__sum_2E_2B_2B_2B_2E2,type,
    c_2Equotient__sum_2E_2B_2B_2B_2E2: du > du > u ).

thf(c_2Equotient__sum_2E_2B_2B_2B_2E4,type,
    c_2Equotient__sum_2E_2B_2B_2B_2E4: du > du > du > du > u ).

thf(c_2Equotient_2E_2D_2D_3E_2E0,type,
    c_2Equotient_2E_2D_2D_3E_2E0: u ).

thf(c_2Equotient_2E_2D_2D_3E_2E3,type,
    c_2Equotient_2E_2D_2D_3E_2E3: du > du > du > u ).

thf(c_2Ebool_2E_2F_5C_2E0,type,
    c_2Ebool_2E_2F_5C_2E0: u ).

thf(c_2Ebool_2E_2F_5C_2E2,type,
    c_2Ebool_2E_2F_5C_2E2: du > du > u ).

thf(c_2Emin_2E_3D_2E0,type,
    c_2Emin_2E_3D_2E0: u ).

thf(c_2Emin_2E_3D_2E2,type,
    c_2Emin_2E_3D_2E2: du > du > u ).

thf(c_2Equotient_2E_3D_3D_3D_3E_2E0,type,
    c_2Equotient_2E_3D_3D_3D_3E_2E0: u ).

thf(c_2Equotient_2E_3D_3D_3D_3E_2E4,type,
    c_2Equotient_2E_3D_3D_3D_3E_2E4: du > du > du > du > u ).

thf(c_2Emin_2E_3D_3D_3E_2E0,type,
    c_2Emin_2E_3D_3D_3E_2E0: u ).

thf(c_2Emin_2E_3D_3D_3E_2E2,type,
    c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).

thf(c_2Ebool_2E_3F_2E0,type,
    c_2Ebool_2E_3F_2E0: u ).

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

thf(c_2Equotient_2EEQUIV_2E0,type,
    c_2Equotient_2EEQUIV_2E0: u ).

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

thf(c_2Ebool_2EF_2E0,type,
    c_2Ebool_2EF_2E0: u ).

thf(c_2Esum_2EINL_2E0,type,
    c_2Esum_2EINL_2E0: u ).

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

thf(c_2Esum_2EINR_2E0,type,
    c_2Esum_2EINR_2E0: u ).

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

thf(c_2Esum_2EISL_2E0,type,
    c_2Esum_2EISL_2E0: u ).

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

thf(c_2Esum_2EISR_2E0,type,
    c_2Esum_2EISR_2E0: u ).

thf(c_2Esum_2EISR_2E1,type,
    c_2Esum_2EISR_2E1: du > u ).

thf(c_2Equotient_2EQUOTIENT_2E0,type,
    c_2Equotient_2EQUOTIENT_2E0: u ).

thf(c_2Equotient_2EQUOTIENT_2E3,type,
    c_2Equotient_2EQUOTIENT_2E3: du > du > du > u ).

thf(c_2Ebool_2ET_2E0,type,
    c_2Ebool_2ET_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E0,type,
    c_2Ebool_2E_5C_2F_2E0: u ).

thf(c_2Ebool_2E_5C_2F_2E2,type,
    c_2Ebool_2E_5C_2F_2E2: du > du > u ).

thf(c_2Ebool_2E_7E_2E0,type,
    c_2Ebool_2E_7E_2E0: u ).

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

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).

thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).

thf(mono_2Ec_2Ebool_2E_2F_5C,type,
    mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).

thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
    mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).

thf(mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

thf(mono_2Ec_2Ebool_2E_5C_2F,type,
    mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).

thf(mono_2Ec_2Ebool_2E_7E,type,
    mono_2Ec_2Ebool_2E_7E: $o > $o ).

thf(i_mono_2Etyop_2Emin_2Ebool,type,
    i_mono_2Etyop_2Emin_2Ebool: $o > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).

thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).

thf(j_mono_2Etyop_2Emin_2Ebool,type,
    j_mono_2Etyop_2Emin_2Ebool: du > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).

thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
    j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).

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

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

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

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

thf(reserved_2Elogic_2E_2F_5C,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
    <=> ( V0
        & V1 ) ) ).

thf(reserved_2Elogic_2E_5C_2F,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
    <=> ( V0
        | V1 ) ) ).

thf(reserved_2Elogic_2E_7E,axiom,
    ! [V0: $o] :
      ( ( mono_2Ec_2Ebool_2E_7E @ V0 )
    <=> ( (~) @ V0 ) ) ).

thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
    ! [V0: $o,V1: $o] :
      ( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
    <=> ( V0
       => V1 ) ) ).

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

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

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

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

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

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

thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
      = V0 ) ).

thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
    ! [V0: $o > $o > $o] :
      ( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
      = V0 ) ).

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

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b_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_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_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] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_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] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27b_20mono_2EA_27d_20mono_2EA_27f_20mono_2EA_27h,axiom,
    ! [A_27b: d,A_27d: d,A_27f: d,A_27h: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Esum_2E_2B_2B_2E3_2Emono_2EA_27c_20mono_2EA_27d_20mono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27e_20mono_2EA_27g_20mono_2EA_27a_20mono_2EA_27c,axiom,
    ! [A_27a: d,A_27c: d,A_27e: d,A_27g: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Esum_2E_2B_2B_2E2_2Emono_2EA_27e_20mono_2EA_27g_20mono_2EA_27f_20mono_2EA_27h,axiom,
    ! [A_27e: d,A_27f: d,A_27g: d,A_27h: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient__sum_2E_2B_2B_2B_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 ) ) ) ) ).

thf(arityeq4_2Ec_2Equotient__sum_2E_2B_2B_2B_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__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient__sum_2E_2B_2B_2B_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 ) ) ) ) ).

thf(arityeq2_2Ec_2Equotient__sum_2E_2B_2B_2B_2E2_2Emono_2EA_27b_20mono_2EA_27d,axiom,
    ! [A_27b: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ 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_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient__sum_2E_2B_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27a_20mono_2EA_27f_20mono_2EA_27e_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,A_27e: d,A_27f: 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_27e ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2EA_27c_20mono_2EA_27h_20mono_2EA_27g_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,A_27g: d,A_27h: 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_27g ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ X2_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2E_2D_2D_3E_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27e_2CA_27g_29_20mono_2Etyop_2Esum_2Esum_28A_27b_2CA_27d_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27f_2CA_27h_29,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,A_27g: d,A_27h: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X2_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) ) ) ) @ c_2Equotient_2E_2D_2D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X2_2E0 ) ) ) ) ).

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

thf(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 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: 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_27c @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ 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_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ X3_2E0 ) ) ) ) ) ).

thf(arityeq4_2Ec_2Equotient_2E_3D_3D_3D_3E_2E4_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27c_29_20mono_2Etyop_2Esum_2Esum_28A_27b_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,X3_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X3_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Equotient_2E_3D_3D_3D_3E_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ X3_2E0 ) ) ) ) ) ).

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

thf(arityeq1_2Ec_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 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2EA_27b,axiom,
    ! [A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EEQUIV_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( 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_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Equotient_2EEQUIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Equotient_2EEQUIV_2E1_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EEQUIV_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ c_2Equotient_2EEQUIV_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27c @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27c @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27b @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27d @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27d @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EISL_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EISL_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EISL_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EISR_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Esum_2EISR_2E1_2Emono_2EA_27c_20mono_2EA_27d,axiom,
    ! [A_27c: d,A_27d: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EISR_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X0_2E0 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27a_20mono_2EA_27e,axiom,
    ! [A_27a: 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_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ 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_27e ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27e @ 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_27e ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ X2_2E0 ) ) ) ) ) ).

thf(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 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27b_20mono_2EA_27f,axiom,
    ! [A_27b: 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_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27f @ 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_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27f @ 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_27f ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27c_20mono_2EA_27g,axiom,
    ! [A_27c: d,A_27g: 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_27g ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ 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_27g ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27g @ 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_27g ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2EA_27d_20mono_2EA_27h,axiom,
    ! [A_27d: d,A_27h: 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_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ X2_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Equotient_2EQUOTIENT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ X2_2E0 ) ) ) ) ) ).

thf(arityeq3_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29_20mono_2Etyop_2Esum_2Esum_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Equotient_2EQUOTIENT_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X2_2E0 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
      = ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
    ! [V0: $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
    ! [V0: $o > $o > $o,V1: $o] :
      ( ( V0 @ V1 )
      = ( V0 @ V1 ) ) ).

thf(thm_2Equotient__sum_2ESUM__REL__ind,axiom,
    ! [A_27a: d,A_27b: d,V0P_2E0: u] :
      ( ( ! [V1R1_2E0: u,V2R2_2E0: u,V3a1_2E0: u,V4a2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V1R1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V2R2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V3a1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V4a2_2E0 ) ) ) ) ) )
        & ! [V5R1_2E0: u,V6R2_2E0: u,V7b1_2E0: u,V8b2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V5R1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V6R2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V7b1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V8b2_2E0 ) ) ) ) ) )
        & ! [V9R1_2E0: u,V10R2_2E0: u,V11a1_2E0: u,V12b2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V9R1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V10R2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V11a1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V12b2_2E0 ) ) ) ) ) )
        & ! [V13R1_2E0: u,V14R2_2E0: u,V15b1_2E0: u,V16a2_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V13R1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V14R2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V15b1_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V16a2_2E0 ) ) ) ) ) ) )
     => ! [V17v_2E0: u,V18v1_2E0: u,V19v2_2E0: u,V20v3_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ 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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V17v_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V18v1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V19v2_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V20v3_2E0 ) ) ) ) ) ).

thf(thm_2Equotient__sum_2ESUM__REL__def,axiom,
    ! [A_27a: d,A_27b: d,V0b2_2E0: u,V1b1_2E0: u,V2a2_2E0: u,V3a1_2E0: u,V4R2_2E0: u,V5R1_2E0: u] :
      ( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V5R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V3a1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2a2_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 ) ) @ V5R1_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) @ ( s @ A_27a @ V2a2_2E0 ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V5R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1b1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0b2_2E0 ) ) ) ) ) )
        = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R2_2E0 ) @ ( s @ A_27b @ V1b1_2E0 ) ) ) @ ( s @ A_27b @ V0b2_2E0 ) ) ) ) )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V5R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V3a1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0b2_2E0 ) ) ) ) ) )
        = mono_2Ec_2Ebool_2EF )
      & ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V5R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V4R2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1b1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2a2_2E0 ) ) ) ) ) )
        = mono_2Ec_2Ebool_2EF ) ) ).

thf(thm_2Equotient__sum_2ESUM__REL__EQ,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) ) ).

thf(thm_2Equotient__sum_2ESUM__EQUIV,axiom,
    ! [A_27a: d,A_27b: d,V0R1_2E0: u,V1R2_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 ) ) @ V0R1_2E0 ) ) ) )
     => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EEQUIV_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V1R2_2E0 ) ) ) )
       => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EEQUIV_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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 ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2ESUM__QUOTIENT,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EINL__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a_2E0: u] :
              ( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27c @ V6a_2E0 ) ) )
              = ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ A_27c @ V6a_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EINL__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a1_2E0: u,V7a2_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0R1_2E0 ) @ ( s @ A_27a @ V6a1_2E0 ) ) ) @ ( s @ A_27a @ V7a2_2E0 ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V6a1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V7a2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EINR__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6b_2E0: u] :
              ( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27d @ V6b_2E0 ) ) )
              = ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) @ ( s @ A_27d @ V6b_2E0 ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EINR__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6b1_2E0: u,V7b2_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ A_27b @ V6b1_2E0 ) ) ) @ ( s @ A_27b @ V7b2_2E0 ) ) ) )
             => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V6b1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V7b2_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EISL__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ V6a_2E0 ) ) ) )
              = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ V6a_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EISL__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a1_2E0: u,V7a2_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ V6a1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V7a2_2E0 ) ) ) )
             => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V6a1_2E0 ) ) ) )
                = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V7a2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EISR__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ V6a_2E0 ) ) ) )
              = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27b ) @ V5rep2_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ V6a_2E0 ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2EISR__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ 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] :
          ( ( 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 ) ) ) )
         => ! [V6a1_2E0: u,V7a2_2E0: u] :
              ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient__sum_2E_2B_2B_2B_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_2Esum_2Esum @ A_27a @ A_27b ) @ V6a1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V7a2_2E0 ) ) ) )
             => ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V6a1_2E0 ) ) ) )
                = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V7a2_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2ESUM__MAP__PRS,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,A_27g: d,A_27h: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ V2rep1_2E0 ) ) ) )
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_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 ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ V5rep2_2E0 ) ) ) )
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_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 ) ) @ V6R3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ V7abs3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ V8rep3_2E0 ) ) ) )
             => ! [V9R4_2E0: u,V10abs4_2E0: u,V11rep4_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ V9R4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ V10abs4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ V11rep4_2E0 ) ) ) )
                 => ! [V12f_2E0: u,V13g_2E0: u] :
                      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ V12f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ V13g_2E0 ) ) )
                      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27g ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ V2rep1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ V8rep3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27f @ A_27h ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ V10abs4_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ V5rep2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27f ) @ V12f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ ( c_2Equotient_2E_2D_2D_3E_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ V7abs3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ V11rep4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27h ) @ V13g_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Equotient__sum_2ESUM__MAP__RSP,axiom,
    ! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,A_27e: d,A_27f: d,A_27g: d,A_27h: d,V0R1_2E0: u,V1abs1_2E0: u,V2rep1_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 ) ) @ V0R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27e ) @ V1abs1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ A_27a ) @ V2rep1_2E0 ) ) ) )
     => ! [V3R2_2E0: u,V4abs2_2E0: u,V5rep2_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 ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27f ) @ V4abs2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ A_27b ) @ V5rep2_2E0 ) ) ) )
         => ! [V6R3_2E0: u,V7abs3_2E0: u,V8rep3_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 ) ) @ V6R3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27g ) @ V7abs3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ A_27c ) @ V8rep3_2E0 ) ) ) )
             => ! [V9R4_2E0: u,V10abs4_2E0: u,V11rep4_2E0: u] :
                  ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ V9R4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ A_27h ) @ V10abs4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ A_27d ) @ V11rep4_2E0 ) ) ) )
                 => ! [V12f1_2E0: u,V13f2_2E0: u,V14g1_2E0: u,V15g2_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 ) ) @ 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 ) @ V12f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V13f2_2E0 ) ) ) )
                        & ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) ) @ V6R3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ V9R4_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V14g1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V15g2_2E0 ) ) ) ) )
                     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2E_3D_3D_3D_3E_2E4 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_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 ) ) @ V6R3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) @ tyop_2Emin_2Ebool ) ) @ ( c_2Equotient__sum_2E_2B_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ V3R2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Emin_2Efun @ A_27d @ tyop_2Emin_2Ebool ) ) @ V9R4_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V12f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V14g1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27d ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V13f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ A_27d ) @ V15g2_2E0 ) ) ) ) ) ) ) ) ) ) ) ).

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