ITP001 Axioms: ITP052^4.ax
%------------------------------------------------------------------------------
% File : ITP052^4 : 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 : semi_ring.ax [Gau19]
% : HL4052^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 224 ( 73 unt; 111 typ; 0 def)
% Number of atoms : 232 ( 176 equ; 1 cnn)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 9142 ( 1 ~; 1 |; 66 &;9033 @)
% ( 16 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 7 avg;9033 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 137 ( 137 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 107 usr; 44 con; 0-4 aty)
% Number of variables : 556 ( 0 ^ 532 !; 24 ?; 556 :)
% 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(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: d > d ).
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: d ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: d > d > d ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: d ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: d > d > d ).
thf(tyop_2Esemi__ring_2Esemi__ring,type,
tyop_2Esemi__ring_2Esemi__ring: 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_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: u ).
thf(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: du > du > u ).
thf(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0: u ).
thf(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2: 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_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: 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_2EARB_2E0,type,
c_2Ebool_2EARB_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: u ).
thf(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: du > u ).
thf(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0: u ).
thf(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0: u ).
thf(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_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_2EK_2E0,type,
c_2Ecombin_2EK_2E0: u ).
thf(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1: du > u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: 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_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_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_2Esemi__ring_2Eis__semi__ring_2E0,type,
c_2Esemi__ring_2Eis__semi__ring_2E0: u ).
thf(c_2Esemi__ring_2Eis__semi__ring_2E1,type,
c_2Esemi__ring_2Eis__semi__ring_2E1: 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_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0,type,
c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0: u ).
thf(c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4,type,
c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4: du > du > du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__CASE_2E0,type,
c_2Esemi__ring_2Esemi__ring__CASE_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__CASE_2E2,type,
c_2Esemi__ring_2Esemi__ring__CASE_2E2: du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR0_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR0_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2,type,
c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2: du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR1_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR1_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E0,type,
c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1,type,
c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2,type,
c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2: du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRM_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM_2E1,type,
c_2Esemi__ring_2Esemi__ring__SRM_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM_2E3,type,
c_2Esemi__ring_2Esemi__ring__SRM_2E3: du > du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1,type,
c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2,type,
c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2: du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRP_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP_2E1,type,
c_2Esemi__ring_2Esemi__ring__SRP_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP_2E3,type,
c_2Esemi__ring_2Esemi__ring__SRP_2E3: du > du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E0,type,
c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1,type,
c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1: du > u ).
thf(c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2,type,
c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2: du > du > u ).
thf(c_2Esemi__ring_2Esemi__ring__size_2E0,type,
c_2Esemi__ring_2Esemi__ring__size_2E0: u ).
thf(c_2Esemi__ring_2Esemi__ring__size_2E2,type,
c_2Esemi__ring_2Esemi__ring__size_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_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool: $o > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
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(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > 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(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
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(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
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(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X1_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(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2Etyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29_29,axiom,
! [A_27a: d,X0: mono_2Etyop_2Enum_2Enum,X1_2E0: u,X2_2E0: u] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ X2_2E0 ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) ) ) @ c_2Eind__type_2ECONSTR_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ X0 ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ c_2Ecombin_2EK_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28tyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29_29_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Eis__semi__ring_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Esemi__ring_2Eis__semi__ring_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27a_20mono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27b_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29_20mono_2Etyop_2Esemi__ring_2Esemi__ring_28A_27a_29,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq4_2Ec_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X3_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) ) ) @ c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X3_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__CASE_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ A_27b @ ( c_2Esemi__ring_2Esemi__ring__CASE_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ X1_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ A_27b ) ) @ c_2Esemi__ring_2Esemi__ring__CASE_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR0_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ A_27a ) @ c_2Esemi__ring_2Esemi__ring__SR0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR1_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ A_27a ) @ c_2Esemi__ring_2Esemi__ring__SR1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SRM_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRM_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esemi__ring_2Esemi__ring__SRM_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRM_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SRP_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRP_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) ) ).
thf(arityeq3_2Ec_2Esemi__ring_2Esemi__ring__SRP_2E3_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) @ ( s @ A_27a @ X2_2E0 ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRP_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).
thf(arityeq1_2Ec_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) ) @ c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Esemi__ring_2Esemi__ring__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esemi__ring_2Esemi__ring__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_2E0 ) ) ) )
= ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Esemi__ring_2Esemi__ring__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ X1_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(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EDATATYPE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EDATATYPE_2E1 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) ) ) ) ).
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(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__TY__DEF,axiom,
! [A_27a: d,F1_2E0: u,F0_2E0: u] :
( ! [V8n: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8n ) ) ) )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ c_2Eind__type_2EBOTTOM_2E0 ) )
=> ( ! [V1a0_27_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ V1a0_27_2E0 ) ) ) )
<=> ! [V2_27semi__ring_27_2E0: u] :
( ! [V3a0_27_2E0: u] :
( ? [V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: u,V7a3_2E0: u] :
( ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ V3a0_27_2E0 )
= ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ ( c_2Eind__type_2ECONSTR_2E3 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ V5a1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_2E0 ) ) ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27semi__ring_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ V3a0_27_2E0 ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27semi__ring_27_2E0 ) @ ( s @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ V1a0_27_2E0 ) ) ) ) ) )
=> ? [V0rep_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Eind__type_2Erecspace @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__case__def,axiom,
! [A_27a: d,A_27b: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a3_2E0: u,V4f_2E0: u] :
( ( s @ A_27b @ ( c_2Esemi__ring_2Esemi__ring__CASE_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ A_27a @ V1a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3a3_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V4f_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V4f_2E0 ) @ ( s @ A_27a @ V0a0_2E0 ) ) ) @ ( s @ A_27a @ V1a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2a2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3a3_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__size__def,axiom,
! [A_27a: d,V0f_2E0: u,V1a0_2E0: u,V2a1_2E0: u,V3a2_2E0: u,V4a3_2E0: u] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Esemi__ring_2Esemi__ring__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ A_27a @ V2a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4a3_2E0 ) ) ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) ) ) ) @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ A_27a @ V2a1_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SR0,axiom,
! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) ) )
= ( s @ A_27a @ V0a_2E0 ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SR1,axiom,
! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) ) )
= ( s @ A_27a @ V1a0_2E0 ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SRP,axiom,
! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SRM,axiom,
! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SR0__fupd,axiom,
! [A_27a: d,V0f1_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SR1__fupd,axiom,
! [A_27a: d,V0f1_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SRP__fupd,axiom,
! [A_27a: d,V0f1_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__SRM__fupd,axiom,
! [A_27a: d,V0f1_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eis__semi__ring__def,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
<=> ( ! [V1n_2E0: u,V2m_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) )
& ! [V3n_2E0: u,V4m_2E0: u,V5p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V4m_2E0 ) @ ( s @ A_27a @ V5p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) @ ( s @ A_27a @ V4m_2E0 ) ) ) @ ( s @ A_27a @ V5p_2E0 ) ) ) )
& ! [V6n_2E0: u,V7m_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) @ ( s @ A_27a @ V7m_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V7m_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) ) ) )
& ! [V8n_2E0: u,V9m_2E0: u,V10p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V8n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V9m_2E0 ) @ ( s @ A_27a @ V10p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V8n_2E0 ) @ ( s @ A_27a @ V9m_2E0 ) ) ) @ ( s @ A_27a @ V10p_2E0 ) ) ) )
& ! [V11n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V11n_2E0 ) ) )
= ( s @ A_27a @ V11n_2E0 ) )
& ! [V12n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V12n_2E0 ) ) )
= ( s @ A_27a @ V12n_2E0 ) )
& ! [V13n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V13n_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
& ! [V14n_2E0: u,V15m_2E0: u,V16p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V14n_2E0 ) @ ( s @ A_27a @ V15m_2E0 ) ) ) @ ( s @ A_27a @ V16p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V14n_2E0 ) @ ( s @ A_27a @ V16p_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V15m_2E0 ) @ ( s @ A_27a @ V16p_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__accessors,axiom,
! [A_27a: d] :
( ! [V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a_2E0 ) @ ( s @ A_27a @ V1a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) ) )
= ( s @ A_27a @ V0a_2E0 ) )
& ! [V4a_2E0: u,V5a0_2E0: u,V6f_2E0: u,V7f0_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V4a_2E0 ) @ ( s @ A_27a @ V5a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f0_2E0 ) ) ) ) )
= ( s @ A_27a @ V5a0_2E0 ) )
& ! [V8a_2E0: u,V9a0_2E0: u,V10f_2E0: u,V11f0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V8a_2E0 ) @ ( s @ A_27a @ V9a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V10f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V11f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V10f_2E0 ) )
& ! [V12a_2E0: u,V13a0_2E0: u,V14f_2E0: u,V15f0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V12a_2E0 ) @ ( s @ A_27a @ V13a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V15f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V15f0_2E0 ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__fn__updates,axiom,
! [A_27a: d] :
( ! [V0f1_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f1_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) )
& ! [V5f1_2E0: u,V6a_2E0: u,V7a0_2E0: u,V8f_2E0: u,V9f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ A_27a @ V7a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V6a_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) @ ( s @ A_27a @ V7a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f0_2E0 ) ) ) )
& ! [V10f1_2E0: u,V11a_2E0: u,V12a0_2E0: u,V13f_2E0: u,V14f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V11a_2E0 ) @ ( s @ A_27a @ V12a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V13f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V14f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V11a_2E0 ) @ ( s @ A_27a @ V12a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V13f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V14f0_2E0 ) ) ) )
& ! [V15f1_2E0: u,V16a_2E0: u,V17a0_2E0: u,V18f_2E0: u,V19f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V15f1_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V16a_2E0 ) @ ( s @ A_27a @ V17a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V18f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V19f0_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V16a_2E0 ) @ ( s @ A_27a @ V17a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V18f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V15f1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V19f0_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__accfupds,axiom,
! [A_27a: d] :
( ! [V0s_2E0: u,V1f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) )
& ! [V2s_2E0: u,V3f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2s_2E0 ) ) ) )
& ! [V4s_2E0: u,V5f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V4s_2E0 ) ) ) )
& ! [V6s_2E0: u,V7f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) )
& ! [V8s_2E0: u,V9f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V9f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V8s_2E0 ) ) ) )
& ! [V10s_2E0: u,V11f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V10s_2E0 ) ) ) )
& ! [V12s_2E0: u,V13f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12s_2E0 ) ) ) )
& ! [V14s_2E0: u,V15f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V15f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V14s_2E0 ) ) ) )
& ! [V16s_2E0: u,V17f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V17f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V16s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V16s_2E0 ) ) ) )
& ! [V18s_2E0: u,V19f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V19f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V18s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V18s_2E0 ) ) ) )
& ! [V20s_2E0: u,V21f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V21f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V20s_2E0 ) ) ) )
& ! [V22s_2E0: u,V23f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V23f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V22s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V22s_2E0 ) ) ) )
& ! [V24s_2E0: u,V25f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V25f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V24s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V25f_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V24s_2E0 ) ) ) ) ) )
& ! [V26s_2E0: u,V27f_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V27f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V26s_2E0 ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V27f_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V26s_2E0 ) ) ) ) ) )
& ! [V28s_2E0: u,V29f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V29f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V28s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V29f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V28s_2E0 ) ) ) ) ) )
& ! [V30s_2E0: u,V31f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V31f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V30s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V31f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V30s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__fupdfupds,axiom,
! [A_27a: d] :
( ! [V0s_2E0: u,V1g_2E0: u,V2f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) )
& ! [V3s_2E0: u,V4g_2E0: u,V5f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3s_2E0 ) ) ) )
& ! [V6s_2E0: u,V7g_2E0: u,V8f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V7g_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) )
& ! [V9s_2E0: u,V10g_2E0: u,V11f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10g_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9s_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__fupdfupds__comp,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0g_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) ) ) )
& ! [V2h_2E0: u,V3g_2E0: u,V4f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V2h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V2h_2E0 ) ) ) )
& ! [V5g_2E0: u,V6f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) ) ) )
& ! [V7h_2E0: u,V8g_2E0: u,V9f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V7h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V7h_2E0 ) ) ) )
& ! [V10g_2E0: u,V11f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V10g_2E0 ) ) ) ) ) )
& ! [V12h_2E0: u,V13g_2E0: u,V14f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V12h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V13g_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V12h_2E0 ) ) ) )
& ! [V15g_2E0: u,V16f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V15g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V15g_2E0 ) ) ) ) ) )
& ! [V17h_2E0: u,V18g_2E0: u,V19f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V19f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V18g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V17h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V19f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V18g_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V17h_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__fupdcanon,axiom,
! [A_27a: d] :
( ! [V0s_2E0: u,V1g_2E0: u,V2f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) ) ) )
& ! [V3s_2E0: u,V4g_2E0: u,V5f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V5f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V3s_2E0 ) ) ) ) ) )
& ! [V6s_2E0: u,V7g_2E0: u,V8f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V8f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V6s_2E0 ) ) ) ) ) )
& ! [V9s_2E0: u,V10g_2E0: u,V11f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V9s_2E0 ) ) ) ) ) )
& ! [V12s_2E0: u,V13g_2E0: u,V14f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V12s_2E0 ) ) ) ) ) )
& ! [V15s_2E0: u,V16g_2E0: u,V17f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V17f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15s_2E0 ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16g_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V17f_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V15s_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__fupdcanon__comp,axiom,
! [A_27a: d,A_27b: d] :
( ! [V0g_2E0: u,V1f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) ) ) ) ) )
& ! [V2h_2E0: u,V3g_2E0: u,V4f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V2h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V2h_2E0 ) ) ) ) ) )
& ! [V5g_2E0: u,V6f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V6f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V6f_2E0 ) ) ) ) ) )
& ! [V7h_2E0: u,V8g_2E0: u,V9f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V9f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V7h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V9f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V7h_2E0 ) ) ) ) ) )
& ! [V10g_2E0: u,V11f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V11f_2E0 ) ) ) ) ) )
& ! [V12h_2E0: u,V13g_2E0: u,V14f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V12h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V14f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V12h_2E0 ) ) ) ) ) )
& ! [V15g_2E0: u,V16f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V15g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V15g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V16f_2E0 ) ) ) ) ) )
& ! [V17h_2E0: u,V18g_2E0: u,V19f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V19f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V18g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V17h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V18g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V19f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V17h_2E0 ) ) ) ) ) )
& ! [V20g_2E0: u,V21f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V21f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V20g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V20g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V21f_2E0 ) ) ) ) ) )
& ! [V22h_2E0: u,V23g_2E0: u,V24f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V24f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V22h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V24f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V22h_2E0 ) ) ) ) ) )
& ! [V25g_2E0: u,V26f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V26f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V25g_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V25g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V26f_2E0 ) ) ) ) ) )
& ! [V27h_2E0: u,V28g_2E0: u,V29f_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V29f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V28g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V27h_2E0 ) ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V28g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ V29f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ V27h_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__component__equality,axiom,
! [A_27a: d,V0s1_2E0: u,V1s2_2E0: u] :
( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s1_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s2_2E0 ) )
<=> ( ( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s1_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s2_2E0 ) ) ) )
& ( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s1_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s2_2E0 ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s2_2E0 ) ) ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s1_2E0 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s2_2E0 ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__updates__eq__literal,axiom,
! [A_27a: d,V0s_2E0: u,V1a0_2E0: u,V2a_2E0: u,V3f0_2E0: u,V4f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__literal__nchotomy,axiom,
! [A_27a: d,V0s_2E0: u] :
? [V1a0_2E0: u,V2a_2E0: u,V3f0_2E0: u,V4f_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0s_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2EFORALL__semi__ring,axiom,
! [A_27a: d,V0P_2E0: u] :
( ! [V1s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s_2E0 ) ) ) )
<=> ! [V2a0_2E0: u,V3a_2E0: u,V4f0_2E0: u,V5f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2EEXISTS__semi__ring,axiom,
! [A_27a: d,V0P_2E0: u] :
( ? [V1s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1s_2E0 ) ) ) )
<=> ? [V2a0_2E0: u,V3a_2E0: u,V4f0_2E0: u,V5f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__literal__11,axiom,
! [A_27a: d,V0a01_2E0: u,V1a1_2E0: u,V2f01_2E0: u,V3f1_2E0: u,V4a02_2E0: u,V5a2_2E0: u,V6f02_2E0: u,V7f2_2E0: u] :
( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V0a01_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a1_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f01_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f1_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V4a02_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SR1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V5a2_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRP__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6f02_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Esemi__ring__SRM__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f2_2E0 ) ) ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) )
<=> ( ( ( s @ A_27a @ V0a01_2E0 )
= ( s @ A_27a @ V4a02_2E0 ) )
& ( ( s @ A_27a @ V1a1_2E0 )
= ( s @ A_27a @ V5a2_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f01_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6f02_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f1_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f2_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Edatatype__semi__ring,axiom,
! [A_27a: d,V0semi__ring_2E0: u,V1record_2E0: u,V2SRP_2E0: u,V3SRM_2E0: u,V4SR1_2E0: u,V5SR0_2E0: u] : ( mono_2Ec_2Ebool_2EDATATYPE_2Emono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ V1record_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0semi__ring_2E0 ) ) ) @ ( s @ A_27a @ V5SR0_2E0 ) ) ) @ ( s @ A_27a @ V4SR1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2SRP_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3SRM_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__11,axiom,
! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a3_2E0: u,V4a0_27_2E0: u,V5a1_27_2E0: u,V6a2_27_2E0: u,V7a3_27_2E0: u] :
( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V0a0_2E0 ) @ ( s @ A_27a @ V1a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3a3_2E0 ) ) )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V4a0_27_2E0 ) @ ( s @ A_27a @ V5a1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_27_2E0 ) ) ) )
<=> ( ( ( s @ A_27a @ V0a0_2E0 )
= ( s @ A_27a @ V4a0_27_2E0 ) )
& ( ( s @ A_27a @ V1a1_2E0 )
= ( s @ A_27a @ V5a1_27_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2a2_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_27_2E0 ) )
& ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3a3_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_27_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__nchotomy,axiom,
! [A_27a: d,V0ss_2E0: u] :
? [V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] :
( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0ss_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__Axiom,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u] :
? [V1fn_2E0: u] :
! [V2a0_2E0: u,V3a1_2E0: u,V4a2_2E0: u,V5a3_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ A_27b ) @ V1fn_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ A_27a @ V3a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5a3_2E0 ) ) ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ A_27a @ V3a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4a2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5a3_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__induction,axiom,
! [A_27a: d,V0P_2E0: u] :
( ! [V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) ) ) )
=> ! [V5s_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V5s_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__case__cong,axiom,
! [A_27a: d,A_27b: d,V0f_27_2E0: u,V1M_2E0: u,V2M_27_2E0: u,V3f_2E0: u] :
( ( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1M_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2M_27_2E0 ) )
& ! [V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: u,V7a3_2E0: u] :
( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2M_27_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ A_27a @ V5a1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_2E0 ) ) ) )
=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V3f_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ A_27a @ V5a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V0f_27_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ A_27a @ V5a1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6a2_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a3_2E0 ) ) ) ) ) )
=> ( ( s @ A_27b @ ( c_2Esemi__ring_2Esemi__ring__CASE_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V1M_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V3f_2E0 ) ) )
= ( s @ A_27b @ ( c_2Esemi__ring_2Esemi__ring__CASE_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V2M_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V0f_27_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Esemi__ring__case__eq,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_2E0: u,V2f_2E0: u] :
( ( ( s @ A_27b @ ( c_2Esemi__ring_2Esemi__ring__CASE_2E2 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0x_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V2f_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) )
<=> ? [V3a_2E0: u,V4a0_2E0: u,V5f_27_2E0: u,V6f0_2E0: u] :
( ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0x_2E0 )
= ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ V3a_2E0 ) @ ( s @ A_27a @ V4a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6f0_2E0 ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ A_27b ) ) ) ) @ V2f_2E0 ) @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ A_27a @ V4a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V5f_27_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V6f0_2E0 ) ) )
= ( s @ A_27b @ V1v_2E0 ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__sym,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u,V2m_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__assoc,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Emult__sym,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u,V2m_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Emult__assoc,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__zero__left,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
= ( s @ A_27a @ V1n_2E0 ) ) ) ).
thf(thm_2Esemi__ring_2Emult__one__left,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
= ( s @ A_27a @ V1n_2E0 ) ) ) ).
thf(thm_2Esemi__ring_2Emult__zero__left,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Edistr__left,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__zero__right,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) ) )
= ( s @ A_27a @ V1n_2E0 ) ) ) ).
thf(thm_2Esemi__ring_2Emult__one__right,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR1_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) ) )
= ( s @ A_27a @ V1n_2E0 ) ) ) ).
thf(thm_2Esemi__ring_2Emult__zero__right,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1n_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SR0_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Edistr__right,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1m_2E0: u,V2n_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__rotate,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1m_2E0: u,V2n_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ V1m_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Eplus__permute,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1m_2E0: u,V2n_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRP_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ V2n_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Emult__rotate,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1m_2E0: u,V2n_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ V1m_2E0 ) ) ) ) ) ).
thf(thm_2Esemi__ring_2Emult__permute,axiom,
! [A_27a: d,V0r_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) ) ) )
=> ! [V1m_2E0: u,V2n_2E0: u,V3p_2E0: u] :
( ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V2n_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
= ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Esemi__ring_2Esemi__ring__SRM_2E3 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ V2n_2E0 ) ) ) ) ) ).
%------------------------------------------------------------------------------