ITP001 Axioms: ITP012^4.ax
%------------------------------------------------------------------------------
% File : ITP012^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : sum.ax [Gau19]
% : HL4012^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 174 ( 61 unt; 77 typ; 0 def)
% Number of atoms : 206 ( 113 equ; 12 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 3917 ( 12 ~; 5 |; 28 &;3827 @)
% ( 27 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 8 avg;3827 nst)
% Number of types : 4 ( 3 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 76 ( 74 usr; 34 con; 0-3 aty)
% Number of variables : 422 ( 0 ^ 412 !; 10 ?; 422 :)
% 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_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_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_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0: u ).
thf(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1: du > u ).
thf(c_2Esum_2EABS__sum_2E0,type,
c_2Esum_2EABS__sum_2E0: u ).
thf(c_2Esum_2EABS__sum_2E1,type,
c_2Esum_2EABS__sum_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0: u ).
thf(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1: du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_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_2Esum_2EIS__SUM__REP_2E0,type,
c_2Esum_2EIS__SUM__REP_2E0: u ).
thf(c_2Esum_2EIS__SUM__REP_2E1,type,
c_2Esum_2EIS__SUM__REP_2E1: du > u ).
thf(c_2Esum_2EOUTL_2E0,type,
c_2Esum_2EOUTL_2E0: u ).
thf(c_2Esum_2EOUTL_2E1,type,
c_2Esum_2EOUTL_2E1: du > u ).
thf(c_2Esum_2EOUTR_2E0,type,
c_2Esum_2EOUTR_2E0: u ).
thf(c_2Esum_2EOUTR_2E1,type,
c_2Esum_2EOUTR_2E1: du > u ).
thf(c_2Esum_2EREP__sum_2E0,type,
c_2Esum_2EREP__sum_2E0: u ).
thf(c_2Esum_2EREP__sum_2E1,type,
c_2Esum_2EREP__sum_2E1: du > u ).
thf(c_2Esum_2ESUM__ALL_2E0,type,
c_2Esum_2ESUM__ALL_2E0: u ).
thf(c_2Esum_2ESUM__ALL_2E3,type,
c_2Esum_2ESUM__ALL_2E3: du > du > du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > 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_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0: u ).
thf(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2: du > du > u ).
thf(c_2Esum_2Esum__CASE_2E0,type,
c_2Esum_2Esum__CASE_2E0: u ).
thf(c_2Esum_2Esum__CASE_2E3,type,
c_2Esum_2Esum__CASE_2E3: du > 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_27b_20mono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) ) ) @ c_2Esum_2E_2B_2B_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ 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_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(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_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esum_2Esum_28A_27a_2CA_27b_29_2CA_27c_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EABS__sum_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_2EABS__sum_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EABS__sum_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27b_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29,axiom,
! [A_27c: d,A_27d: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27d_2CA_27c_29,axiom,
! [A_27c: d,A_27d: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27e_2CA_27f_29,axiom,
! [A_27e: d,A_27f: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esum_2Esum_28A_27g_2CA_27h_29,axiom,
! [A_27g: d,A_27h: d,X0: $o,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ X1_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) ) ) ) @ c_2Ebool_2ECOND_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ X0 ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2EA_27c,axiom,
! [A_27c: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ A_27c @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) @ ( s @ A_27c @ 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_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27b @ 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_2EINL_2E1_2Emono_2EA_27d_20mono_2EA_27c,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27d @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27d @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e: d,A_27f: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27e @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27e @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27e @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINL_2E1_2Emono_2EA_27g_20mono_2EA_27h,axiom,
! [A_27g: d,A_27h: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27g @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27g @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ A_27g @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27a @ 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_27d_20mono_2EA_27c,axiom,
! [A_27c: d,A_27d: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27c @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27c @ 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_2EINR_2E1_2Emono_2EA_27e_20mono_2EA_27f,axiom,
! [A_27e: d,A_27f: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27f @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27f @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27f @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EINR_2E1_2Emono_2EA_27g_20mono_2EA_27h,axiom,
! [A_27g: d,A_27h: d,X0_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27h @ X0_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27h @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ A_27h @ 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_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_2EIS__SUM__REP_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_2EIS__SUM__REP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( 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 @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EIS__SUM__REP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EOUTL_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27a ) @ c_2Esum_2EOUTL_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EOUTR_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ A_27b @ ( c_2Esum_2EOUTR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27b ) @ c_2Esum_2EOUTR_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esum_2EREP__sum_2E1_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Esum_2EREP__sum_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ c_2Esum_2EREP__sum_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esum_2ESUM__ALL_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) @ ( s @ ( 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_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( 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_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Esum_2ESUM__ALL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X2_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27b_2Ctyop_2Emin_2Ebool_29_29_29_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27c,axiom,
! [A_27a: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esum_2Esum_28A_27c_2CA_27d_29_20mono_2EA_27d,axiom,
! [A_27b: d,A_27c: d,A_27d: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ 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 @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2EA_27c_20mono_2Etyop_2Esum_2Esum_28A_27a_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27a: d,A_27b: d,A_27c: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27c @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X2_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ A_27c ) ) ) @ c_2Esum_2Esum__CASE_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ X2_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esum_2Esum__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b_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] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) ) ) @ c_2Esum_2Esum__CASE_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ 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_2Esum_2EIS__SUM__REP,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EIS__SUM__REP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V0f_2E0 ) ) ) )
<=> ? [V1v1_2E0: u,V2v2_2E0: u] :
( ! [V3x: $o,V4x_27_2E0: u,V5x_27_27_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_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V0f_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V3x ) ) ) ) @ ( s @ A_27a @ V4x_27_2E0 ) ) ) @ ( s @ A_27b @ V5x_27_27_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V4x_27_2E0 )
= ( s @ A_27a @ V1v1_2E0 ) )
& V3x ) )
| ! [V6x: $o,V7x_27_2E0: u,V8x_27_27_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_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V0f_2E0 ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V6x ) ) ) ) @ ( s @ A_27a @ V7x_27_2E0 ) ) ) @ ( s @ A_27b @ V8x_27_27_2E0 ) ) ) )
<=> ( ( ( s @ A_27b @ V8x_27_27_2E0 )
= ( s @ A_27b @ V2v2_2E0 ) )
& ( (~) @ V6x ) ) ) ) ) ).
thf(thm_2Esum_2Esum__TY__DEF,axiom,
! [A_27a: d,A_27b: d] :
? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ tyop_2Emin_2Ebool ) @ c_2Esum_2EIS__SUM__REP_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ V0rep_2E0 ) ) ) ) ).
thf(thm_2Esum_2Esum__ISO__DEF,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0a_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EABS__sum_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Esum_2EREP__sum_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0a_2E0 ) )
& ! [V1r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EIS__SUM__REP_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V1r_2E0 ) ) ) )
<=> ( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( c_2Esum_2EREP__sum_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EABS__sum_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V1r_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ V1r_2E0 ) ) ) ) ).
thf(thm_2Esum_2EINL__DEF,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0e_2E0: u,V1b: $o,V2x_2E0: u,V3y_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_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0e_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1b ) ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V3y_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V2x_2E0 )
= ( s @ A_27a @ V0e_2E0 ) )
& V1b ) )
=> ! [V0e_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0e_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EABS__sum_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27a @ V0e_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esum_2EINR__DEF,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V0e_2E0: u,V1b: $o,V2x_2E0: u,V3y_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_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V0e_2E0 ) ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1b ) ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ V3y_2E0 ) ) ) )
<=> ( ( ( s @ A_27b @ V3y_2E0 )
= ( s @ A_27b @ V0e_2E0 ) )
& ( (~) @ V1b ) ) )
=> ! [V0e_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0e_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EABS__sum_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) ) @ F0_2E0 ) @ ( s @ A_27b @ V0e_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esum_2EISL,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) ) )
& ! [V1y_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Esum_2EISR,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0x_2E0 ) ) ) ) ) )
& ! [V1y_2E0: u] : ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1y_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Esum_2EOUTL,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( s @ A_27a @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(thm_2Esum_2EOUTR,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( s @ A_27b @ ( c_2Esum_2EOUTR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0x_2E0 ) ) ) ) )
= ( s @ A_27b @ V0x_2E0 ) ) ).
thf(thm_2Esum_2Esum__case__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d] :
( ! [V0x_2E0: u,V1f_2E0: u,V2f1_2E0: u] :
( ( s @ A_27c @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V2f1_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) )
& ! [V3y_2E0: u,V4f_2E0: u,V5f1_2E0: u] :
( ( s @ A_27c @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V3y_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V5f1_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V5f1_2E0 ) @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__MAP__def,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d] :
( ! [V0f_2E0: u,V1g_2E0: u,V2a_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27a @ V2a_2E0 ) ) ) ) ) )
& ! [V3f_2E0: u,V4g_2E0: u,V5b_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4g_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V5b_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V4g_2E0 ) @ ( s @ A_27b @ V5b_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__ALL__def,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0P_2E0: u,V1Q_2E0: u,V2x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1Q_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) )
& ! [V3P_2E0: u,V4Q_2E0: u,V5y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V4Q_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V5y_2E0 ) ) ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V4Q_2E0 ) @ ( s @ A_27b @ V5y_2E0 ) ) ) ) ) ) ).
thf(thm_2Esum_2EINL__11,axiom,
! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1x_2E0 )
= ( s @ A_27a @ V0y_2E0 ) ) ) ).
thf(thm_2Esum_2EINR__11,axiom,
! [A_27a: d,A_27b: d,V0y_2E0: u,V1x_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V0y_2E0 ) ) ) )
<=> ( ( s @ A_27b @ V1x_2E0 )
= ( s @ A_27b @ V0y_2E0 ) ) ) ).
thf(thm_2Esum_2EINR__INL__11,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0y_2E0: u,V1x_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0y_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V1x_2E0 )
= ( s @ A_27a @ V0y_2E0 ) ) )
& ! [V2y_2E0: u,V3x_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V3x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V2y_2E0 ) ) ) )
<=> ( ( s @ A_27b @ V3x_2E0 )
= ( s @ A_27b @ V2y_2E0 ) ) ) ) ).
thf(thm_2Esum_2EINR__neq__INL,axiom,
! [A_27a: d,A_27b: d,V0v1_2E0: u,V1v2_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1v2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0v1_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2Esum__axiom,axiom,
! [A_27a: d,A_27b: d,A_27c: d,F0_2E0: u] :
( ! [V0f_2E0: u,V1g_2E0: u,V2h_2E0: u] :
( ( 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 ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ V2h_2E0 ) ) ) )
<=> ( ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINL_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ V2h_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINR_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1g_2E0 ) ) ) )
=> ! [V0f_2E0: u,V1g_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ tyop_2Emin_2Ebool ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1g_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esum_2Esum__INDUCT,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ( ! [V1x_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) )
& ! [V2y_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ) )
=> ! [V3s_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V3s_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2EFORALL__SUM,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ! [V1s_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_2E0 ) ) ) )
<=> ( ! [V2x_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
& ! [V3y_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Esum_2EEXISTS__SUM,axiom,
! [A_27a: d,A_27b: d,V0P_2E0: u] :
( ? [V1s_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_2E0 ) ) ) )
<=> ( ? [V2x_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) )
| ? [V3y_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 ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V3y_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Esum_2Esum__Axiom,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u] :
? [V2h_2E0: u] :
( ! [V3x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ V2h_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V3x_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27a @ V3x_2E0 ) ) ) )
& ! [V4y_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ A_27c ) @ V2h_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V4y_2E0 ) ) ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V1g_2E0 ) @ ( s @ A_27b @ V4y_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2Esum__CASES,axiom,
! [A_27a: d,A_27b: d,V0ss_2E0: u] :
( ? [V1x_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0ss_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) )
| ? [V2y_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0ss_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V2y_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2Esum__distinct,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1y_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2Esum__distinct1,axiom,
! [A_27a: d,A_27b: d,V0v1_2E0: u,V1v2_2E0: u] :
( (~)
@ ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V1v2_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V0v1_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2EISL__OR__ISR,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2EINL,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ).
thf(thm_2Esum_2EINR,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ ( c_2Esum_2EOUTR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ).
thf(thm_2Esum_2Esum__case__cong,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f1_27_2E0: u,V1f_27_2E0: u,V2M_2E0: u,V3M_27_2E0: u,V4f_2E0: u,V5f1_2E0: u] :
( ( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2M_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V3M_27_2E0 ) )
& ! [V6x_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V3M_27_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V6x_2E0 ) ) ) )
=> ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V4f_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_27_2E0 ) @ ( s @ A_27a @ V6x_2E0 ) ) ) ) )
& ! [V7y_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V3M_27_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V7y_2E0 ) ) ) )
=> ( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V5f1_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f1_27_2E0 ) @ ( s @ A_27b @ V7y_2E0 ) ) ) ) ) )
=> ( ( s @ A_27c @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2M_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V5f1_2E0 ) ) )
= ( s @ A_27c @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V3M_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V1f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ V0f1_27_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__MAP,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2z_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ A_27a @ ( c_2Esum_2EOUTL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27d @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ A_27b @ ( c_2Esum_2EOUTR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__MAP__CASE,axiom,
! [A_27a: d,A_27b: d,A_27c: d,A_27d: d,V0f_2E0: u,V1g_2E0: u,V2z_2E0: u] :
( ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2E_2B_2B_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) @ ( c_2Esum_2Esum__CASE_2E3 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V2z_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27c @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ c_2Esum_2EINL_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27d @ ( tyop_2Esum_2Esum @ A_27c @ A_27d ) ) @ c_2Esum_2EINR_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27d ) @ V1g_2E0 ) ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__MAP__I,axiom,
! [A_27a: d,A_27b: d] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( c_2Esum_2E_2B_2B_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ c_2Ecombin_2EI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27b ) @ c_2Ecombin_2EI_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Ecombin_2EI_2E0 ) ) ).
thf(thm_2Esum_2Econd__sum__expand,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,V0P: $o] :
( ! [V1x_2E0: u,V2y_2E0: u,V3z_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27a @ V1x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27b @ V2y_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27b @ A_27a ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27a @ V3z_2E0 ) ) ) )
<=> ( V0P
& ( ( s @ A_27a @ V3z_2E0 )
= ( s @ A_27a @ V1x_2E0 ) ) ) )
& ! [V4x_2E0: u,V5y_2E0: u,V6z_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27c @ V4x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27d @ V5y_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27d @ A_27c ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27d @ V6z_2E0 ) ) ) )
<=> ( ( (~) @ V0P )
& ( ( s @ A_27d @ V6z_2E0 )
= ( s @ A_27d @ V5y_2E0 ) ) ) )
& ! [V7x_2E0: u,V8y_2E0: u,V9z_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27e @ V7x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27f @ V8y_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27e @ A_27f ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27e @ V9z_2E0 ) ) ) )
<=> ( V0P
& ( ( s @ A_27e @ V9z_2E0 )
= ( s @ A_27e @ V7x_2E0 ) ) ) )
& ! [V10x_2E0: u,V11y_2E0: u,V12z_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0P ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27g @ V10x_2E0 ) ) ) @ ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27h @ V11y_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esum_2Esum @ A_27g @ A_27h ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27h @ V12z_2E0 ) ) ) )
<=> ( ( (~) @ V0P )
& ( ( s @ A_27h @ V12z_2E0 )
= ( s @ A_27h @ V11y_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2ENOT__ISL__ISR,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2ENOT__ISR__ISL,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u] :
( ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISR_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2EISL_2E1 @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0x_2E0 ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__ALL__MONO,axiom,
! [A_27a: d,A_27b: d,V0s_2E0: u,V1Q_27_2E0: u,V2Q_2E0: u,V3P_27_2E0: u,V4P_2E0: u] :
( ( ! [V5x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4P_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_27_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
& ! [V6y_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1Q_27_2E0 ) @ ( s @ A_27b @ V6y_2E0 ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V2Q_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V1Q_27_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) ) ) ) ).
thf(thm_2Esum_2ESUM__ALL__CONG,axiom,
! [A_27a: d,A_27b: d,V0s_2E0: u,V1s_27_2E0: u,V2P_2E0: u,V3P_27_2E0: u,V4Q_2E0: u,V5Q_27_2E0: u] :
( ( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0s_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_27_2E0 ) )
& ! [V6a_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_27_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINL_2E1 @ ( s @ A_27a @ V6a_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_27_2E0 ) @ ( s @ A_27a @ V6a_2E0 ) ) ) ) ) )
& ! [V7b_2E0: u] :
( ( ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_27_2E0 )
= ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ ( c_2Esum_2EINR_2E1 @ ( s @ A_27b @ V7b_2E0 ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V4Q_2E0 ) @ ( s @ A_27b @ V7b_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Q_27_2E0 ) @ ( s @ A_27b @ V7b_2E0 ) ) ) ) ) ) )
=> ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V4Q_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V0s_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esum_2ESUM__ALL_2E3 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3P_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Q_27_2E0 ) @ ( s @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) @ V1s_27_2E0 ) ) ) ) ) ) ).
thf(thm_2Esum_2Edatatype__sum,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0sum_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ A_27c ) ) @ V0sum_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINL_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esum_2Esum @ A_27a @ A_27b ) ) @ c_2Esum_2EINR_2E0 ) ) ) ) ) ) ).
%------------------------------------------------------------------------------