%------------------------------------------------------------------------------
% File     : ITP074^4 : TPTP v9.0.0. Bugfixed v7.5.0.
% Domain   : Interactive Theorem Proving
% Axioms   : HOL4 syntactic export, chainy mode
% Version  : [BG+19] axioms.
% English  :

% Refs     : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
%          : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source   : [BG+19]
% Names    : ring.ax [Gau19]
%          : HL4074^4.ax [TPAP]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  248 (  86 unt; 124 typ;   0 def)
%            Number of atoms       :  272 ( 215 equ;   1 cnn)
%            Maximal formula atoms :   25 (   1 avg)
%            Number of connectives : 12062 (   1   ~;   1   |;  95   &;11926   @)
%                                         (  16 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   40 (   7 avg;11926 nst)
%            Number of types       :    5 (   4 usr)
%            Number of type conns  :  151 ( 151   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  122 ( 120 usr;  49 con; 0-5 aty)
%            Number of variables   :  685 (   0   ^ 656   !;  29   ?; 685   :)
% 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_2Ering_2Ering,type,
    tyop_2Ering_2Ering: 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_2Ering_2Eis__ring_2E0,type,
    c_2Ering_2Eis__ring_2E0: u ).

thf(c_2Ering_2Eis__ring_2E1,type,
    c_2Ering_2Eis__ring_2E1: 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_2Ering_2Erecordtype_2Ering_2E0,type,
    c_2Ering_2Erecordtype_2Ering_2E0: u ).

thf(c_2Ering_2Erecordtype_2Ering_2E5,type,
    c_2Ering_2Erecordtype_2Ering_2E5: du > du > du > 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_2Ering_2Ering__CASE_2E0,type,
    c_2Ering_2Ering__CASE_2E0: u ).

thf(c_2Ering_2Ering__CASE_2E2,type,
    c_2Ering_2Ering__CASE_2E2: du > du > u ).

thf(c_2Ering_2Ering__R0_2E0,type,
    c_2Ering_2Ering__R0_2E0: u ).

thf(c_2Ering_2Ering__R0_2E1,type,
    c_2Ering_2Ering__R0_2E1: du > u ).

thf(c_2Ering_2Ering__R0__fupd_2E0,type,
    c_2Ering_2Ering__R0__fupd_2E0: u ).

thf(c_2Ering_2Ering__R0__fupd_2E1,type,
    c_2Ering_2Ering__R0__fupd_2E1: du > u ).

thf(c_2Ering_2Ering__R0__fupd_2E2,type,
    c_2Ering_2Ering__R0__fupd_2E2: du > du > u ).

thf(c_2Ering_2Ering__R1_2E0,type,
    c_2Ering_2Ering__R1_2E0: u ).

thf(c_2Ering_2Ering__R1_2E1,type,
    c_2Ering_2Ering__R1_2E1: du > u ).

thf(c_2Ering_2Ering__R1__fupd_2E0,type,
    c_2Ering_2Ering__R1__fupd_2E0: u ).

thf(c_2Ering_2Ering__R1__fupd_2E1,type,
    c_2Ering_2Ering__R1__fupd_2E1: du > u ).

thf(c_2Ering_2Ering__R1__fupd_2E2,type,
    c_2Ering_2Ering__R1__fupd_2E2: du > du > u ).

thf(c_2Ering_2Ering__RM_2E0,type,
    c_2Ering_2Ering__RM_2E0: u ).

thf(c_2Ering_2Ering__RM_2E1,type,
    c_2Ering_2Ering__RM_2E1: du > u ).

thf(c_2Ering_2Ering__RM_2E3,type,
    c_2Ering_2Ering__RM_2E3: du > du > du > u ).

thf(c_2Ering_2Ering__RM__fupd_2E0,type,
    c_2Ering_2Ering__RM__fupd_2E0: u ).

thf(c_2Ering_2Ering__RM__fupd_2E1,type,
    c_2Ering_2Ering__RM__fupd_2E1: du > u ).

thf(c_2Ering_2Ering__RM__fupd_2E2,type,
    c_2Ering_2Ering__RM__fupd_2E2: du > du > u ).

thf(c_2Ering_2Ering__RN_2E0,type,
    c_2Ering_2Ering__RN_2E0: u ).

thf(c_2Ering_2Ering__RN_2E1,type,
    c_2Ering_2Ering__RN_2E1: du > u ).

thf(c_2Ering_2Ering__RN_2E2,type,
    c_2Ering_2Ering__RN_2E2: du > du > u ).

thf(c_2Ering_2Ering__RN__fupd_2E0,type,
    c_2Ering_2Ering__RN__fupd_2E0: u ).

thf(c_2Ering_2Ering__RN__fupd_2E1,type,
    c_2Ering_2Ering__RN__fupd_2E1: du > u ).

thf(c_2Ering_2Ering__RN__fupd_2E2,type,
    c_2Ering_2Ering__RN__fupd_2E2: du > du > u ).

thf(c_2Ering_2Ering__RP_2E0,type,
    c_2Ering_2Ering__RP_2E0: u ).

thf(c_2Ering_2Ering__RP_2E1,type,
    c_2Ering_2Ering__RP_2E1: du > u ).

thf(c_2Ering_2Ering__RP_2E3,type,
    c_2Ering_2Ering__RP_2E3: du > du > du > u ).

thf(c_2Ering_2Ering__RP__fupd_2E0,type,
    c_2Ering_2Ering__RP__fupd_2E0: u ).

thf(c_2Ering_2Ering__RP__fupd_2E1,type,
    c_2Ering_2Ering__RP__fupd_2E1: du > u ).

thf(c_2Ering_2Ering__RP__fupd_2E2,type,
    c_2Ering_2Ering__RP__fupd_2E2: du > du > u ).

thf(c_2Ering_2Ering__size_2E0,type,
    c_2Ering_2Ering__size_2E0: u ).

thf(c_2Ering_2Ering__size_2E2,type,
    c_2Ering_2Ering__size_2E2: du > du > u ).

thf(c_2Ering_2Esemi__ring__of_2E0,type,
    c_2Ering_2Esemi__ring__of_2E0: u ).

thf(c_2Ering_2Esemi__ring__of_2E1,type,
    c_2Ering_2Esemi__ring__of_2E1: 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_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2CA_27a_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 @ 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 @ 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 @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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 @ 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_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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 @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( 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 @ A_27a ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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 @ A_27a ) ) @ ( tyop_2Epair_2Eprod @ ( 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 @ A_27a ) ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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 @ 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_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) )
      = ( 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_2EK_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod_28tyop_2Emin_2Efun_28A_27a_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28A_27a_2CA_27a_29_29_29_29_29_29_20mono_2Etyop_2Ering_2Ering_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Ering_2Ering @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Eis__ring_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ c_2Ering_2Eis__ring_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_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_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2CA_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X1_2E0 ) ) )
      = ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( 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_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29,axiom,
    ! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2Etyop_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29_20mono_2Etyop_2Ering_2Ering_28A_27a_29,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) ) @ c_2Ecombin_2Eo_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq5_2Ec_2Ering_2Erecordtype_2Ering_2E5_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u,X3_2E0: u,X4_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ X4_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Ering_2Ering @ 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 @ A_27a ) @ ( tyop_2Ering_2Ering @ 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) ) ) ) @ c_2Ering_2Erecordtype_2Ering_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 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X4_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_2Ering_2Ering__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_2Ering_2Ering__CASE_2E2 @ ( s @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ A_27b ) ) @ c_2Ering_2Ering__CASE_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R0_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ A_27a ) @ c_2Ering_2Ering__R0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R0__fupd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__R0__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__R0__fupd_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__R0__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R1_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ A_27a ) @ c_2Ering_2Ering__R1_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__R1__fupd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__R1__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__R1__fupd_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__R1__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RM_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_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RM_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ering_2Ering__RM_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RM_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RM__fupd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RM__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_2Ering_2Ering__RM__fupd_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RN_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ c_2Ering_2Ering__RN_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__RN_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) @ ( s @ A_27a @ X1_2E0 ) ) )
      = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ c_2Ering_2Ering__RN_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RN__fupd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RN__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__RN__fupd_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RN__fupd_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RP_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_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RP_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) ) ).

thf(arityeq3_2Ec_2Ering_2Ering__RP_2E3_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u,X2_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) @ c_2Ering_2Ering__RP_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) @ ( s @ A_27a @ X2_2E0 ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Ering__RP__fupd_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RP__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_2Ering_2Ering__RP__fupd_2E2_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u,X1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) ) @ c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ).

thf(arityeq2_2Ec_2Ering_2Ering__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_2Ering_2Ering__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) )
      = ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Enum_2Enum ) ) @ c_2Ering_2Ering__size_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X1_2E0 ) ) ) ) ) ).

thf(arityeq1_2Ec_2Ering_2Esemi__ring__of_2E1_2Emono_2EA_27a,axiom,
    ! [A_27a: d,X0_2E0: u] :
      ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_2E0 ) ) )
      = ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) ) @ c_2Ering_2Esemi__ring__of_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ X0_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_2Ering_2Ering__TY__DEF,axiom,
    ! [A_27a: d,F1_2E0: u,F0_2E0: u] :
      ( ! [V9n: 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ F1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V9n ) ) ) )
          = ( 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ V1a0_27_2E0 ) ) ) )
          <=> ! [V2_27ring_27_2E0: u] :
                ( ! [V3a0_27_2E0: u] :
                    ( ? [V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: u,V7a3_2E0: u,V8a4_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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 ) ) @ V7a3_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8a4_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ring_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ V2_27ring_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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) @ tyop_2Emin_2Ebool ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) ) ) ) ) ) @ V0rep_2E0 ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__case__def,axiom,
    ! [A_27a: d,A_27b: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a3_2E0: u,V4a4_2E0: u,V5f_2E0: u] :
      ( ( s @ A_27b @ ( c_2Ering_2Ering__CASE_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4a4_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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ V5f_2E0 ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ V5f_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 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4a4_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__size__def,axiom,
    ! [A_27a: d,V0f_2E0: u,V1a0_2E0: u,V2a1_2E0: u,V3a2_2E0: u,V4a3_2E0: u,V5a4_2E0: u] :
      ( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( c_2Ering_2Ering__size_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Enum_2Enum ) @ V0f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5a4_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_2Ering_2Ering__R0,axiom,
    ! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
      = ( s @ A_27a @ V0a_2E0 ) ) ).

thf(thm_2Ering_2Ering__R1,axiom,
    ! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
      ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
      = ( s @ A_27a @ V1a0_2E0 ) ) ).

thf(thm_2Ering_2Ering__RP,axiom,
    ! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f_2E0 ) ) ).

thf(thm_2Ering_2Ering__RM,axiom,
    ! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f0_2E0 ) ) ).

thf(thm_2Ering_2Ering__RN,axiom,
    ! [A_27a: d,V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
      ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f1_2E0 ) ) ).

thf(thm_2Ering_2Ering__R0__fupd,axiom,
    ! [A_27a: d,V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__R1__fupd,axiom,
    ! [A_27a: d,V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__RP__fupd,axiom,
    ! [A_27a: d,V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 ) ) ) @ V0f2_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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__RM__fupd,axiom,
    ! [A_27a: d,V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 ) ) ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4f0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__RN__fupd,axiom,
    ! [A_27a: d,V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_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 ) ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ) ) ).

thf(thm_2Ering_2Eis__ring__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
    <=> ( ! [V1n_2E0: u,V2m_2E0: u] :
            ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V3n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V4m_2E0 ) @ ( s @ A_27a @ V5p_2E0 ) ) ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V6n_2E0 ) @ ( s @ A_27a @ V7m_2E0 ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V8n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V9m_2E0 ) @ ( s @ A_27a @ V10p_2E0 ) ) ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ 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_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V11n_2E0 ) ) )
            = ( s @ A_27a @ V11n_2E0 ) )
        & ! [V12n_2E0: u] :
            ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V12n_2E0 ) ) )
            = ( s @ A_27a @ V12n_2E0 ) )
        & ! [V13n_2E0: u] :
            ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V13n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V13n_2E0 ) ) ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
        & ! [V14n_2E0: u,V15m_2E0: u,V16p_2E0: u] :
            ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V14n_2E0 ) @ ( s @ A_27a @ V15m_2E0 ) ) ) @ ( s @ A_27a @ V16p_2E0 ) ) )
            = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V14n_2E0 ) @ ( s @ A_27a @ V16p_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V15m_2E0 ) @ ( s @ A_27a @ V16p_2E0 ) ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Esemi__ring__of__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) )
      = ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Esemi__ring_2Erecordtype_2Esemi__ring_2E4 @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__accessors,axiom,
    ! [A_27a: d] :
      ( ! [V0a_2E0: u,V1a0_2E0: u,V2f_2E0: u,V3f0_2E0: u,V4f1_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4f1_2E0 ) ) ) ) )
          = ( s @ A_27a @ V0a_2E0 ) )
      & ! [V5a_2E0: u,V6a0_2E0: u,V7f_2E0: u,V8f0_2E0: u,V9f1_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V5a_2E0 ) @ ( s @ A_27a @ V6a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V8f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f1_2E0 ) ) ) ) )
          = ( s @ A_27a @ V6a0_2E0 ) )
      & ! [V10a_2E0: u,V11a0_2E0: u,V12f_2E0: u,V13f0_2E0: u,V14f1_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V10a_2E0 ) @ ( s @ A_27a @ V11a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V12f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V13f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V14f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V12f_2E0 ) )
      & ! [V15a_2E0: u,V16a0_2E0: u,V17f_2E0: u,V18f0_2E0: u,V19f1_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V15a_2E0 ) @ ( s @ A_27a @ V16a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V17f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V18f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V19f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V18f0_2E0 ) )
      & ! [V20a_2E0: u,V21a0_2E0: u,V22f_2E0: u,V23f0_2E0: u,V24f1_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V20a_2E0 ) @ ( s @ A_27a @ V21a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V22f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V24f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V24f1_2E0 ) ) ) ).

thf(thm_2Ering_2Ering__fn__updates,axiom,
    ! [A_27a: d] :
      ( ! [V0f2_2E0: u,V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0f2_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 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) )
      & ! [V6f2_2E0: u,V7a_2E0: u,V8a0_2E0: u,V9f_2E0: u,V10f0_2E0: u,V11f1_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V7a_2E0 ) @ ( s @ A_27a @ V8a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V10f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V11f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V7a_2E0 ) @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f2_2E0 ) @ ( s @ A_27a @ V8a0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V9f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V10f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V11f1_2E0 ) ) ) )
      & ! [V12f2_2E0: u,V13a_2E0: u,V14a0_2E0: u,V15f_2E0: u,V16f0_2E0: u,V17f1_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V12f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27a @ V14a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V15f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V16f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V17f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V13a_2E0 ) @ ( s @ A_27a @ V14a0_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 ) ) ) @ V12f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V15f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V16f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V17f1_2E0 ) ) ) )
      & ! [V18f2_2E0: u,V19a_2E0: u,V20a0_2E0: u,V21f_2E0: u,V22f0_2E0: u,V23f1_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V18f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ A_27a @ V20a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V21f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V22f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V19a_2E0 ) @ ( s @ A_27a @ V20a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V21f_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 ) ) ) @ V18f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V22f0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23f1_2E0 ) ) ) )
      & ! [V24f2_2E0: u,V25a_2E0: u,V26a0_2E0: u,V27f_2E0: u,V28f0_2E0: u,V29f1_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V24f2_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V25a_2E0 ) @ ( s @ A_27a @ V26a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V27f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V28f0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V29f1_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V25a_2E0 ) @ ( s @ A_27a @ V26a0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V27f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V28f0_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 ) ) @ V24f2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V29f1_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__accfupds,axiom,
    ! [A_27a: d] :
      ( ! [V0r_2E0: u,V1f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
      & ! [V2r_2E0: u,V3f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V2r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V2r_2E0 ) ) ) )
      & ! [V4r_2E0: u,V5f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V4r_2E0 ) ) ) )
      & ! [V6r_2E0: u,V7f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) )
      & ! [V8r_2E0: u,V9f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V8r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V8r_2E0 ) ) ) )
      & ! [V10r_2E0: u,V11f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V10r_2E0 ) ) ) )
      & ! [V12r_2E0: u,V13f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V13f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) )
      & ! [V14r_2E0: u,V15f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V15f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V14r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V14r_2E0 ) ) ) )
      & ! [V16r_2E0: u,V17f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V17f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V16r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V16r_2E0 ) ) ) )
      & ! [V18r_2E0: u,V19f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V19f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V18r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V18r_2E0 ) ) ) )
      & ! [V20r_2E0: u,V21f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V21f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V20r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V20r_2E0 ) ) ) )
      & ! [V22r_2E0: u,V23f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V22r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V22r_2E0 ) ) ) )
      & ! [V24r_2E0: u,V25f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V25f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V24r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V24r_2E0 ) ) ) )
      & ! [V26r_2E0: u,V27f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V27f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V26r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V26r_2E0 ) ) ) )
      & ! [V28r_2E0: u,V29f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V28r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V28r_2E0 ) ) ) )
      & ! [V30r_2E0: u,V31f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V31f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V30r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V30r_2E0 ) ) ) )
      & ! [V32r_2E0: u,V33f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V33f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V32r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V32r_2E0 ) ) ) )
      & ! [V34r_2E0: u,V35f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V35f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V34r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V34r_2E0 ) ) ) )
      & ! [V36r_2E0: u,V37f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V37f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V36r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V36r_2E0 ) ) ) )
      & ! [V38r_2E0: u,V39f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V39f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V38r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V38r_2E0 ) ) ) )
      & ! [V40r_2E0: u,V41f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V41f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V40r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V41f_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V40r_2E0 ) ) ) ) ) )
      & ! [V42r_2E0: u,V43f_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V43f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V42r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V43f_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V42r_2E0 ) ) ) ) ) )
      & ! [V44r_2E0: u,V45f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V45f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V44r_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 ) ) ) @ V45f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V44r_2E0 ) ) ) ) ) )
      & ! [V46r_2E0: u,V47f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V47f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V46r_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 ) ) ) @ V47f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V46r_2E0 ) ) ) ) ) )
      & ! [V48r_2E0: u,V49f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V49f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V48r_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 ) ) @ V49f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V48r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__fupdfupds,axiom,
    ! [A_27a: d] :
      ( ! [V0r_2E0: u,V1g_2E0: u,V2f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__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_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
      & ! [V3r_2E0: u,V4g_2E0: u,V5f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V3r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__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_2Ering_2Ering @ A_27a ) @ V3r_2E0 ) ) ) )
      & ! [V6r_2E0: u,V7g_2E0: u,V8f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) )
      & ! [V9r_2E0: u,V10g_2E0: u,V11f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V9r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V9r_2E0 ) ) ) )
      & ! [V12r_2E0: u,V13g_2E0: u,V14f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V13g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V14f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__fupdfupds__comp,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0g_2E0: u,V1f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V2h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__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_2Ering_2Ering @ A_27a ) ) @ V2h_2E0 ) ) ) )
      & ! [V5g_2E0: u,V6f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V7h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__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_2Ering_2Ering @ A_27a ) ) @ V7h_2E0 ) ) ) )
      & ! [V10g_2E0: u,V11f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ V12h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ V12h_2E0 ) ) ) )
      & ! [V15g_2E0: u,V16f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ V17h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ V17h_2E0 ) ) ) )
      & ! [V20g_2E0: u,V21f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V21f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V20g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V21f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V20g_2E0 ) ) ) ) ) )
      & ! [V22h_2E0: u,V23g_2E0: u,V24f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V24f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V22h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V24f_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23g_2E0 ) ) ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V22h_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__fupdcanon,axiom,
    ! [A_27a: d] :
      ( ! [V0r_2E0: u,V1g_2E0: u,V2f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V2f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) )
      & ! [V3r_2E0: u,V4g_2E0: u,V5f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V3r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V3r_2E0 ) ) ) ) ) )
      & ! [V6r_2E0: u,V7g_2E0: u,V8f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) ) ) )
      & ! [V9r_2E0: u,V10g_2E0: u,V11f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V9r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V9r_2E0 ) ) ) ) ) )
      & ! [V12r_2E0: u,V13g_2E0: u,V14f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V12r_2E0 ) ) ) ) ) )
      & ! [V15r_2E0: u,V16g_2E0: u,V17f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ V15r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ V15r_2E0 ) ) ) ) ) )
      & ! [V18r_2E0: u,V19g_2E0: u,V20f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V20f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V19g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V18r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V19g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V20f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V18r_2E0 ) ) ) ) ) )
      & ! [V21r_2E0: u,V22g_2E0: u,V23f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V22g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V21r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V22g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V23f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V21r_2E0 ) ) ) ) ) )
      & ! [V24r_2E0: u,V25g_2E0: u,V26f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V26f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V25g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V24r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V25g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V26f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V24r_2E0 ) ) ) ) ) )
      & ! [V27r_2E0: u,V28g_2E0: u,V29f_2E0: u] :
          ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V29f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V28g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V27r_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V28g_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V29f_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V27r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__fupdcanon__comp,axiom,
    ! [A_27a: d,A_27b: d] :
      ( ! [V0g_2E0: u,V1f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V1f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V0g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V2h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V2h_2E0 ) ) ) ) ) )
      & ! [V5g_2E0: u,V6f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V7h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ V7h_2E0 ) ) ) ) ) )
      & ! [V10g_2E0: u,V11f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V10g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V12h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V13g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ V12h_2E0 ) ) ) ) ) )
      & ! [V15g_2E0: u,V16f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V15g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V15g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V18g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V17h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V18g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ V17h_2E0 ) ) ) ) ) )
      & ! [V20g_2E0: u,V21f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V20g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V20g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V22h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V23g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ V22h_2E0 ) ) ) ) ) )
      & ! [V25g_2E0: u,V26f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ V27h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) ) @ V27h_2E0 ) ) ) ) ) )
      & ! [V30g_2E0: u,V31f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V31f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V30g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V30g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V31f_2E0 ) ) ) ) ) )
      & ! [V32h_2E0: u,V33g_2E0: u,V34f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V34f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V33g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V32h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R0__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V33g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V34f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V32h_2E0 ) ) ) ) ) )
      & ! [V35g_2E0: u,V36f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V36f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V35g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V35g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V36f_2E0 ) ) ) ) ) )
      & ! [V37h_2E0: u,V38g_2E0: u,V39f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V39f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V38g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V37h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__R1__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V38g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V39f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V37h_2E0 ) ) ) ) ) )
      & ! [V40g_2E0: u,V41f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V41f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V40g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V40g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V41f_2E0 ) ) ) ) ) )
      & ! [V42h_2E0: u,V43g_2E0: u,V44f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V44f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V43g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V42h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RP__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 ) ) ) @ V43g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V44f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V42h_2E0 ) ) ) ) ) )
      & ! [V45g_2E0: u,V46f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V46f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V45g_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V45g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V46f_2E0 ) ) ) ) ) )
      & ! [V47h_2E0: u,V48g_2E0: u,V49f_2E0: u] :
          ( ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V49f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V48g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V47h_2E0 ) ) ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RM__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 ) ) ) @ V48g_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ecombin_2Eo_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ ( tyop_2Ering_2Ering @ A_27a ) ) @ ( c_2Ering_2Ering__RN__fupd_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V49f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Ering_2Ering @ A_27a ) ) @ V47h_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__component__equality,axiom,
    ! [A_27a: d,V0r1_2E0: u,V1r2_2E0: u] :
      ( ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 )
        = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) )
    <=> ( ( ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) ) ) )
        & ( ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RP_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ering_2Ering__RM_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) ) ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r1_2E0 ) ) )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ering_2Ering__RN_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r2_2E0 ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__updates__eq__literal,axiom,
    ! [A_27a: d,V0r_2E0: u,V1a0_2E0: u,V2a_2E0: u,V3f1_2E0: u,V4f0_2E0: u,V5f_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ) ) ) ) )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__literal__nchotomy,axiom,
    ! [A_27a: d,V0r_2E0: u] :
    ? [V1a0_2E0: u,V2a_2E0: u,V3f1_2E0: u,V4f0_2E0: u,V5f_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V5f_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ering_2EFORALL__ring,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1r_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r_2E0 ) ) ) )
    <=> ! [V2a0_2E0: u,V3a_2E0: u,V4f1_2E0: u,V5f0_2E0: u,V6f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) @ V4f1_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) @ V5f0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ering_2EEXISTS__ring,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ? [V1r_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V1r_2E0 ) ) ) )
    <=> ? [V2a0_2E0: u,V3a_2E0: u,V4f1_2E0: u,V5f0_2E0: u,V6f_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V2a0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V3a_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) @ V4f1_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) @ V5f0_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6f_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Ering__literal__11,axiom,
    ! [A_27a: d,V0a01_2E0: u,V1a1_2E0: u,V2f11_2E0: u,V3f01_2E0: u,V4f1_2E0: u,V5a02_2E0: u,V6a2_2E0: u,V7f12_2E0: u,V8f02_2E0: u,V9f2_2E0: u] :
      ( ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V0a01_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V1a1_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) @ V2f11_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) @ V3f01_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f1_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) )
        = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R0__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V5a02_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__R1__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ A_27a @ V6a2_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RP__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 ) ) @ V7f12_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RM__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 ) ) @ V8f02_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Ering__RN__fupd_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ ( c_2Ecombin_2EK_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f2_2E0 ) ) ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ c_2Ebool_2EARB_2E0 ) ) ) ) ) ) ) ) ) ) ) )
    <=> ( ( ( s @ A_27a @ V0a01_2E0 )
          = ( s @ A_27a @ V5a02_2E0 ) )
        & ( ( s @ A_27a @ V1a1_2E0 )
          = ( s @ A_27a @ V6a2_2E0 ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2f11_2E0 )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7f12_2E0 ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V3f01_2E0 )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V8f02_2E0 ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4f1_2E0 )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9f2_2E0 ) ) ) ) ).

thf(thm_2Ering_2Edatatype__ring,axiom,
    ! [A_27a: d,V0ring_2E0: u,V1record_2E0: u,V2RP_2E0: u,V3RN_2E0: u,V4RM_2E0: u,V5R1_2E0: u,V6R0_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 @ 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 @ 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_2Efun @ ( 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_2Efun @ ( 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_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ 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_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ tyop_2Emin_2Ebool ) ) ) ) ) ) @ V1record_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0ring_2E0 ) ) ) @ ( s @ A_27a @ V6R0_2E0 ) ) ) @ ( s @ A_27a @ V5R1_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V2RP_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V4RM_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V3RN_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__11,axiom,
    ! [A_27a: d,V0a0_2E0: u,V1a1_2E0: u,V2a2_2E0: u,V3a3_2E0: u,V4a4_2E0: u,V5a0_27_2E0: u,V6a1_27_2E0: u,V7a2_27_2E0: u,V8a3_27_2E0: u,V9a4_27_2E0: u] :
      ( ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ A_27a ) @ V4a4_2E0 ) ) )
        = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( s @ A_27a @ V5a0_27_2E0 ) @ ( s @ A_27a @ V6a1_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V7a2_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) ) @ V8a3_27_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9a4_27_2E0 ) ) ) )
    <=> ( ( ( s @ A_27a @ V0a0_2E0 )
          = ( s @ A_27a @ V5a0_27_2E0 ) )
        & ( ( s @ A_27a @ V1a1_2E0 )
          = ( s @ A_27a @ V6a1_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 ) ) @ V7a2_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 ) ) @ V8a3_27_2E0 ) )
        & ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V4a4_2E0 )
          = ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V9a4_27_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__nchotomy,axiom,
    ! [A_27a: d,V0rr_2E0: u] :
    ? [V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] :
      ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0rr_2E0 )
      = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__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,V6a4_2E0: u] :
      ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ A_27b ) @ V1fn_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6a4_2E0 ) ) ) ) )
      = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V6a4_2E0 ) ) ) ) ).

thf(thm_2Ering_2Ering__induction,axiom,
    ! [A_27a: d,V0P_2E0: u] :
      ( ! [V1a_2E0: u,V2a0_2E0: u,V3f_2E0: u,V4f0_2E0: u,V5f1_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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_2Emin_2Efun @ A_27a @ A_27a ) @ V5f1_2E0 ) ) ) ) ) )
     => ! [V6r_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Ering_2Ering @ A_27a ) @ tyop_2Emin_2Ebool ) @ V0P_2E0 ) @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V6r_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__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_2Ering_2Ering @ A_27a ) @ V1M_2E0 )
          = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V2M_27_2E0 ) )
        & ! [V4a0_2E0: u,V5a1_2E0: u,V6a2_2E0: u,V7a3_2E0: u,V8a4_2E0: u] :
            ( ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V2M_27_2E0 )
              = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8a4_2E0 ) ) ) )
           => ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8a4_2E0 ) ) )
              = ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V8a4_2E0 ) ) ) ) ) )
     => ( ( s @ A_27b @ ( c_2Ering_2Ering__CASE_2E2 @ ( s @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ V3f_2E0 ) ) )
        = ( s @ A_27b @ ( c_2Ering_2Ering__CASE_2E2 @ ( s @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ A_27b ) ) ) ) ) @ V0f_27_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__case__eq,axiom,
    ! [A_27a: d,A_27b: d,V0x_2E0: u,V1v_2E0: u,V2f_2E0: u] :
      ( ( ( s @ A_27b @ ( c_2Ering_2Ering__CASE_2E2 @ ( s @ ( tyop_2Ering_2Ering @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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,V7f1_2E0: u] :
          ( ( ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0x_2E0 )
            = ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ ( c_2Ering_2Erecordtype_2Ering_2E5 @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7f1_2E0 ) ) ) )
          & ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( 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 @ 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 ) ) @ ( tyop_2Emin_2Efun @ ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ V7f1_2E0 ) ) )
            = ( s @ A_27b @ V1v_2E0 ) ) ) ) ).

thf(thm_2Ering_2Eplus__sym,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u,V2m_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Eplus__assoc,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Emult__sym,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u,V2m_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Emult__assoc,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Eplus__zero__left,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
          = ( s @ A_27a @ V1n_2E0 ) ) ) ).

thf(thm_2Ering_2Emult__one__left,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
          = ( s @ A_27a @ V1n_2E0 ) ) ) ).

thf(thm_2Ering_2Eopp__def,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Edistr__left,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u,V2m_2E0: u,V3p_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) ) ) @ ( s @ A_27a @ V3p_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V2m_2E0 ) @ ( s @ A_27a @ V3p_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Eplus__zero__right,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RP_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ A_27a @ V1n_2E0 ) ) ) ).

thf(thm_2Ering_2Emult__zero__left,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) @ ( s @ A_27a @ V1n_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Emult__zero__right,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__R0_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ).

thf(thm_2Ering_2Ering__is__semi__ring,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Esemi__ring_2Eis__semi__ring_2E1 @ ( s @ ( tyop_2Esemi__ring_2Esemi__ring @ A_27a ) @ ( c_2Ering_2Esemi__ring__of_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) ) ) ) ).

thf(thm_2Ering_2Emult__one__right,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1n_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1n_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__R1_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) ) )
          = ( s @ A_27a @ V1n_2E0 ) ) ) ).

thf(thm_2Ering_2Eneg__mult,axiom,
    ! [A_27a: d,V0r_2E0: u] :
      ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ering_2Eis__ring_2E1 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) ) ) )
     => ! [V1a_2E0: u,V2b_2E0: u] :
          ( ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) ) ) @ ( s @ A_27a @ V2b_2E0 ) ) )
          = ( s @ A_27a @ ( c_2Ering_2Ering__RN_2E2 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ ( c_2Ering_2Ering__RM_2E3 @ ( s @ ( tyop_2Ering_2Ering @ A_27a ) @ V0r_2E0 ) @ ( s @ A_27a @ V1a_2E0 ) @ ( s @ A_27a @ V2b_2E0 ) ) ) ) ) ) ) ).

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