ITP001 Axioms: ITP085^4.ax
%------------------------------------------------------------------------------
% File : ITP085^4 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : integer.ax [Gau19]
% : HL4085^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 899 ( 330 unt; 349 typ; 0 def)
% Number of atoms : 1524 ( 789 equ; 93 cnn)
% Maximal formula atoms : 30 ( 1 avg)
% Number of connectives : 8135 ( 93 ~; 36 |; 293 &;7441 @)
% ( 127 <=>; 145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg;7441 nst)
% Number of types : 7 ( 6 usr)
% Number of type conns : 1009 (1009 >; 0 *; 0 +; 0 <<)
% Number of symbols : 345 ( 343 usr; 87 con; 0-4 aty)
% Number of variables : 1112 ( 0 ^1090 !; 22 ?;1112 :)
% 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_2Einteger_2Eint,type,
mono_2Etyop_2Einteger_2Eint: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: $tType ).
thf(tyop_2Einteger_2Eint,type,
tyop_2Einteger_2Eint: 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(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_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: u ).
thf(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: du > 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_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: u ).
thf(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_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_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: u ).
thf(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_2Ebool_2E_3F_21_2E0,type,
c_2Ebool_2E_3F_21_2E0: u ).
thf(c_2Ebool_2E_3F_21_2E1,type,
c_2Ebool_2E_3F_21_2E1: du > u ).
thf(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0: u ).
thf(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1: du > u ).
thf(c_2Einteger_2EABS_2E0,type,
c_2Einteger_2EABS_2E0: u ).
thf(c_2Einteger_2EABS_2E1,type,
c_2Einteger_2EABS_2E1: du > 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_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: u ).
thf(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: du > u ).
thf(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: u ).
thf(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: du > du > u ).
thf(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: u ).
thf(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: du > u ).
thf(c_2Earithmetic_2EEXP_2E0,type,
c_2Earithmetic_2EEXP_2E0: u ).
thf(c_2Earithmetic_2EEXP_2E2,type,
c_2Earithmetic_2EEXP_2E2: du > du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0: u ).
thf(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1: du > u ).
thf(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0: u ).
thf(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1: du > u ).
thf(c_2Einteger_2ELEAST__INT_2E0,type,
c_2Einteger_2ELEAST__INT_2E0: u ).
thf(c_2Einteger_2ELEAST__INT_2E1,type,
c_2Einteger_2ELEAST__INT_2E1: du > u ).
thf(c_2Earithmetic_2EMAX_2E0,type,
c_2Earithmetic_2EMAX_2E0: u ).
thf(c_2Earithmetic_2EMAX_2E2,type,
c_2Earithmetic_2EMAX_2E2: du > du > u ).
thf(c_2Earithmetic_2EMIN_2E0,type,
c_2Earithmetic_2EMIN_2E0: u ).
thf(c_2Earithmetic_2EMIN_2E2,type,
c_2Earithmetic_2EMIN_2E2: du > du > u ).
thf(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: u ).
thf(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: du > 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_2Einteger_2ENum_2E0,type,
c_2Einteger_2ENum_2E0: u ).
thf(c_2Einteger_2ENum_2E1,type,
c_2Einteger_2ENum_2E1: du > u ).
thf(c_2Earithmetic_2EODD_2E0,type,
c_2Earithmetic_2EODD_2E0: u ).
thf(c_2Earithmetic_2EODD_2E1,type,
c_2Earithmetic_2EODD_2E1: du > u ).
thf(c_2Equotient_2EQUOTIENT_2E0,type,
c_2Equotient_2EQUOTIENT_2E0: u ).
thf(c_2Equotient_2EQUOTIENT_2E3,type,
c_2Equotient_2EQUOTIENT_2E3: du > du > du > u ).
thf(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0: u ).
thf(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1: du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_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_2Epred__set_2EUNIV_2E0,type,
c_2Epred__set_2EUNIV_2E0: 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_2Enumeral_2EiZ_2E0,type,
c_2Enumeral_2EiZ_2E0: u ).
thf(c_2Enumeral_2EiZ_2E1,type,
c_2Enumeral_2EiZ_2E1: du > u ).
thf(c_2Einteger_2Eint__0_2E0,type,
c_2Einteger_2Eint__0_2E0: u ).
thf(c_2Einteger_2Eint__1_2E0,type,
c_2Einteger_2Eint__1_2E0: u ).
thf(c_2Einteger_2Eint__ABS_2E0,type,
c_2Einteger_2Eint__ABS_2E0: u ).
thf(c_2Einteger_2Eint__ABS_2E1,type,
c_2Einteger_2Eint__ABS_2E1: du > u ).
thf(c_2Einteger_2Eint__ABS__CLASS_2E0,type,
c_2Einteger_2Eint__ABS__CLASS_2E0: u ).
thf(c_2Einteger_2Eint__ABS__CLASS_2E1,type,
c_2Einteger_2Eint__ABS__CLASS_2E1: du > u ).
thf(c_2Einteger_2Eint__REP_2E0,type,
c_2Einteger_2Eint__REP_2E0: u ).
thf(c_2Einteger_2Eint__REP_2E1,type,
c_2Einteger_2Eint__REP_2E1: du > u ).
thf(c_2Einteger_2Eint__REP__CLASS_2E0,type,
c_2Einteger_2Eint__REP__CLASS_2E0: u ).
thf(c_2Einteger_2Eint__REP__CLASS_2E1,type,
c_2Einteger_2Eint__REP__CLASS_2E1: du > u ).
thf(c_2Einteger_2Eint__add_2E0,type,
c_2Einteger_2Eint__add_2E0: u ).
thf(c_2Einteger_2Eint__add_2E2,type,
c_2Einteger_2Eint__add_2E2: du > du > u ).
thf(c_2Einteger_2Eint__div_2E0,type,
c_2Einteger_2Eint__div_2E0: u ).
thf(c_2Einteger_2Eint__div_2E2,type,
c_2Einteger_2Eint__div_2E2: du > du > u ).
thf(c_2Einteger_2Eint__divides_2E0,type,
c_2Einteger_2Eint__divides_2E0: u ).
thf(c_2Einteger_2Eint__divides_2E2,type,
c_2Einteger_2Eint__divides_2E2: du > du > u ).
thf(c_2Einteger_2Eint__exp_2E0,type,
c_2Einteger_2Eint__exp_2E0: u ).
thf(c_2Einteger_2Eint__exp_2E2,type,
c_2Einteger_2Eint__exp_2E2: du > du > u ).
thf(c_2Einteger_2Eint__ge_2E0,type,
c_2Einteger_2Eint__ge_2E0: u ).
thf(c_2Einteger_2Eint__ge_2E2,type,
c_2Einteger_2Eint__ge_2E2: du > du > u ).
thf(c_2Einteger_2Eint__gt_2E0,type,
c_2Einteger_2Eint__gt_2E0: u ).
thf(c_2Einteger_2Eint__gt_2E2,type,
c_2Einteger_2Eint__gt_2E2: du > du > u ).
thf(c_2Einteger_2Eint__le_2E0,type,
c_2Einteger_2Eint__le_2E0: u ).
thf(c_2Einteger_2Eint__le_2E2,type,
c_2Einteger_2Eint__le_2E2: du > du > u ).
thf(c_2Einteger_2Eint__lt_2E0,type,
c_2Einteger_2Eint__lt_2E0: u ).
thf(c_2Einteger_2Eint__lt_2E2,type,
c_2Einteger_2Eint__lt_2E2: du > du > u ).
thf(c_2Einteger_2Eint__max_2E0,type,
c_2Einteger_2Eint__max_2E0: u ).
thf(c_2Einteger_2Eint__max_2E2,type,
c_2Einteger_2Eint__max_2E2: du > du > u ).
thf(c_2Einteger_2Eint__min_2E0,type,
c_2Einteger_2Eint__min_2E0: u ).
thf(c_2Einteger_2Eint__min_2E2,type,
c_2Einteger_2Eint__min_2E2: du > du > u ).
thf(c_2Einteger_2Eint__mod_2E0,type,
c_2Einteger_2Eint__mod_2E0: u ).
thf(c_2Einteger_2Eint__mod_2E2,type,
c_2Einteger_2Eint__mod_2E2: du > du > u ).
thf(c_2Einteger_2Eint__mul_2E0,type,
c_2Einteger_2Eint__mul_2E0: u ).
thf(c_2Einteger_2Eint__mul_2E2,type,
c_2Einteger_2Eint__mul_2E2: du > du > u ).
thf(c_2Einteger_2Eint__neg_2E0,type,
c_2Einteger_2Eint__neg_2E0: u ).
thf(c_2Einteger_2Eint__neg_2E1,type,
c_2Einteger_2Eint__neg_2E1: du > u ).
thf(c_2Einteger_2Eint__of__num_2E0,type,
c_2Einteger_2Eint__of__num_2E0: u ).
thf(c_2Einteger_2Eint__of__num_2E1,type,
c_2Einteger_2Eint__of__num_2E1: du > u ).
thf(c_2Einteger_2Eint__quot_2E0,type,
c_2Einteger_2Eint__quot_2E0: u ).
thf(c_2Einteger_2Eint__quot_2E2,type,
c_2Einteger_2Eint__quot_2E2: du > du > u ).
thf(c_2Einteger_2Eint__rem_2E0,type,
c_2Einteger_2Eint__rem_2E0: u ).
thf(c_2Einteger_2Eint__rem_2E2,type,
c_2Einteger_2Eint__rem_2E2: du > du > u ).
thf(c_2Einteger_2Eint__sub_2E0,type,
c_2Einteger_2Eint__sub_2E0: u ).
thf(c_2Einteger_2Eint__sub_2E2,type,
c_2Einteger_2Eint__sub_2E2: du > du > u ).
thf(c_2Einteger_2Etint__0_2E0,type,
c_2Einteger_2Etint__0_2E0: u ).
thf(c_2Einteger_2Etint__1_2E0,type,
c_2Einteger_2Etint__1_2E0: u ).
thf(c_2Einteger_2Etint__add_2E0,type,
c_2Einteger_2Etint__add_2E0: u ).
thf(c_2Einteger_2Etint__add_2E2,type,
c_2Einteger_2Etint__add_2E2: du > du > u ).
thf(c_2Einteger_2Etint__eq_2E0,type,
c_2Einteger_2Etint__eq_2E0: u ).
thf(c_2Einteger_2Etint__eq_2E1,type,
c_2Einteger_2Etint__eq_2E1: du > u ).
thf(c_2Einteger_2Etint__eq_2E2,type,
c_2Einteger_2Etint__eq_2E2: du > du > u ).
thf(c_2Einteger_2Etint__lt_2E0,type,
c_2Einteger_2Etint__lt_2E0: u ).
thf(c_2Einteger_2Etint__lt_2E2,type,
c_2Einteger_2Etint__lt_2E2: du > du > u ).
thf(c_2Einteger_2Etint__mul_2E0,type,
c_2Einteger_2Etint__mul_2E0: u ).
thf(c_2Einteger_2Etint__mul_2E2,type,
c_2Einteger_2Etint__mul_2E2: du > du > u ).
thf(c_2Einteger_2Etint__neg_2E0,type,
c_2Einteger_2Etint__neg_2E0: u ).
thf(c_2Einteger_2Etint__neg_2E1,type,
c_2Einteger_2Etint__neg_2E1: du > u ).
thf(c_2Einteger_2Etint__of__num_2E0,type,
c_2Einteger_2Etint__of__num_2E0: u ).
thf(c_2Einteger_2Etint__of__num_2E1,type,
c_2Einteger_2Etint__of__num_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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o > $o ) > $o > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ) > ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
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_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Earithmetic_2E_2A,type,
mono_2Ec_2Earithmetic_2E_2A: 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_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Earithmetic_2E_2D,type,
mono_2Ec_2Earithmetic_2E_2D: 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_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2E_3C_3D,type,
mono_2Ec_2Earithmetic_2E_3C_3D: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2EABS,type,
mono_2Ec_2Einteger_2EABS: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EBIT2,type,
mono_2Ec_2Earithmetic_2EBIT2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool: $o > $o > $o > $o ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint: $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Earithmetic_2EDIV,type,
mono_2Ec_2Earithmetic_2EDIV: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EEVEN,type,
mono_2Ec_2Earithmetic_2EEVEN: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EEXP,type,
mono_2Ec_2Earithmetic_2EEXP: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Einteger_2Eint > $o ) > $o ).
thf(mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Einteger_2ELEAST__INT,type,
mono_2Ec_2Einteger_2ELEAST__INT: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Earithmetic_2EMAX,type,
mono_2Ec_2Earithmetic_2EMAX: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EMIN,type,
mono_2Ec_2Earithmetic_2EMIN: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EMOD,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Einteger_2ENum,type,
mono_2Ec_2Einteger_2ENum: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2EODD,type,
mono_2Ec_2Earithmetic_2EODD: mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Equotient_2EQUOTIENT_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Equotient_2EQUOTIENT_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > $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_2Enumeral_2EiZ,type,
mono_2Ec_2Enumeral_2EiZ: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Einteger_2Eint__0,type,
mono_2Ec_2Einteger_2Eint__0: mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__1,type,
mono_2Ec_2Einteger_2Eint__1: mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__ABS,type,
mono_2Ec_2Einteger_2Eint__ABS: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__ABS__CLASS,type,
mono_2Ec_2Einteger_2Eint__ABS__CLASS: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__REP,type,
mono_2Ec_2Einteger_2Eint__REP: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Eint__REP__CLASS,type,
mono_2Ec_2Einteger_2Eint__REP__CLASS: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Ec_2Einteger_2Eint__add,type,
mono_2Ec_2Einteger_2Eint__add: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__div,type,
mono_2Ec_2Einteger_2Eint__div: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__divides,type,
mono_2Ec_2Einteger_2Eint__divides: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__exp,type,
mono_2Ec_2Einteger_2Eint__exp: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__ge,type,
mono_2Ec_2Einteger_2Eint__ge: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__gt,type,
mono_2Ec_2Einteger_2Eint__gt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__le,type,
mono_2Ec_2Einteger_2Eint__le: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__lt,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(mono_2Ec_2Einteger_2Eint__max,type,
mono_2Ec_2Einteger_2Eint__max: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__min,type,
mono_2Ec_2Einteger_2Eint__min: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__mod,type,
mono_2Ec_2Einteger_2Eint__mod: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__mul,type,
mono_2Ec_2Einteger_2Eint__mul: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__neg,type,
mono_2Ec_2Einteger_2Eint__neg: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__of__num,type,
mono_2Ec_2Einteger_2Eint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__quot,type,
mono_2Ec_2Einteger_2Eint__quot: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__rem,type,
mono_2Ec_2Einteger_2Eint__rem: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Eint__sub,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Einteger_2Etint__0,type,
mono_2Ec_2Einteger_2Etint__0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Etint__1,type,
mono_2Ec_2Einteger_2Etint__1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Etint__add,type,
mono_2Ec_2Einteger_2Etint__add: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Etint__eq,type,
mono_2Ec_2Einteger_2Etint__eq: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Ec_2Einteger_2Etint__lt,type,
mono_2Ec_2Einteger_2Etint__lt: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(mono_2Ec_2Einteger_2Etint__mul,type,
mono_2Ec_2Einteger_2Etint__mul: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Etint__neg,type,
mono_2Ec_2Einteger_2Etint__neg: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(mono_2Ec_2Einteger_2Etint__of__num,type,
mono_2Ec_2Einteger_2Etint__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( $o > $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: ( $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29: ( ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29: ( ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ) > 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > u ).
thf(i_mono_2Etyop_2Einteger_2Eint,type,
i_mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > 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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > $o > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: du > $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29: du > ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Einteger_2Eint > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29: du > ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Einteger_2Eint > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint ).
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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
thf(j_mono_2Etyop_2Einteger_2Eint,type,
j_mono_2Etyop_2Einteger_2Eint: du > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ).
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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ V0_2E0 ) ) ) )
= ( s @ tyop_2Einteger_2Eint @ 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(ij_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ 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_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: $o > $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,axiom,
! [V0: $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Einteger_2Eint @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ 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(ji_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_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(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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o > $o,V1: $o] :
( ( 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 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_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_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > $o,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_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_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_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_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2E_3F_21_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_21_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2E_3F_21_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Einteger_2Eint_29 @ mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Einteger_2Eint ) @ c_2Emin_2E_40_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Enum_2Enum ) @ c_2Emin_2E_40_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E0_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ c_2Emin_2E_40_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( c_2Emin_2E_40_2E1 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( 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_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o,V1: $o,V2: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: $o,V1: mono_2Etyop_2Einteger_2Eint,V2: mono_2Etyop_2Einteger_2Eint] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EFINITE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Epred__set_2EFINITE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ c_2Epair_2EFST_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Equotient_2EQUOTIENT_2E0_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Equotient_2EQUOTIENT_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ tyop_2Emin_2Ebool ) ) ) @ c_2Equotient_2EQUOTIENT_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Equotient_2EQUOTIENT_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint,V2: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Equotient_2EQUOTIENT_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Equotient_2EQUOTIENT_2E3 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29 @ V1 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V2 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E0_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Enum_2Enum_29 @ mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Enum_2Enum ) @ c_2Epair_2ESND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E0_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epred__set_2EUNIV_2E0_2Emono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ tyop_2Emin_2Ebool ) @ c_2Epred__set_2EUNIV_2E0 ) ) ).
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_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: $o > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > $o,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint ) > ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( 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_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Einteger_2Eint,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(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Einteger_2Eint__ge,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__ge @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2Eint__gt,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__gt @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2Eint__le,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
<=> ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Einteger_2Eint__sub,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2Etint__0,axiom,
( mono_2Ec_2Einteger_2Etint__0
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Einteger_2Etint__1,axiom,
( mono_2Ec_2Einteger_2Etint__1
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Einteger_2Etint__neg,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__neg @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0x @ V1y ) )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2Etint__add,axiom,
! [V0x1: mono_2Etyop_2Enum_2Enum,V1y1: mono_2Etyop_2Enum_2Enum,V2x2: mono_2Etyop_2Enum_2Enum,V3y2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0x1 @ V1y1 ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V2x2 @ V3y2 ) )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x1 @ V2x2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V1y1 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2Etint__mul,axiom,
! [V0x1: mono_2Etyop_2Enum_2Enum,V1y1: mono_2Etyop_2Enum_2Enum,V2x2: mono_2Etyop_2Enum_2Enum,V3y2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__mul @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0x1 @ V1y1 ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V2x2 @ V3y2 ) )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V0x1 @ V2x2 ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V1y1 @ V3y2 ) ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V0x1 @ V3y2 ) @ ( mono_2Ec_2Earithmetic_2E_2A @ V1y1 @ V2x2 ) ) ) ) ).
thf(thm_2Einteger_2Etint__lt,axiom,
! [V0x1: mono_2Etyop_2Enum_2Enum,V1y1: mono_2Etyop_2Enum_2Enum,V2x2: mono_2Etyop_2Enum_2Enum,V3y2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__lt @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0x1 @ V1y1 ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V2x2 @ V3y2 ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x1 @ V3y2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2x2 @ V1y1 ) ) ) ).
thf(thm_2Einteger_2Etint__eq,axiom,
! [V0x1: mono_2Etyop_2Enum_2Enum,V1y1: mono_2Etyop_2Enum_2Enum,V2x2: mono_2Etyop_2Enum_2Enum,V3y2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V0x1 @ V1y1 ) @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ V2x2 @ V3y2 ) )
<=> ( ( mono_2Ec_2Earithmetic_2E_2B @ V0x1 @ V3y2 )
= ( mono_2Ec_2Earithmetic_2E_2B @ V2x2 @ V1y1 ) ) ) ).
thf(thm_2Einteger_2Etint__of__num,axiom,
( ( ( mono_2Ec_2Einteger_2Etint__of__num @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Einteger_2Etint__0 )
& ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__of__num @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
= ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Einteger_2Etint__of__num @ V0n ) @ mono_2Ec_2Einteger_2Etint__1 ) ) ) ).
thf(thm_2Einteger_2Eint__TY__DEF,axiom,
! [F0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o ) > $o] :
( ! [V1c: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ( F0 @ V1c )
<=> ? [V2r: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V2r @ V2r )
& ( V1c
= ( mono_2Ec_2Einteger_2Etint__eq @ V2r ) ) ) )
=> ? [V0rep: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] : ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Einteger_2Eint @ F0 @ V0rep ) ) ).
thf(thm_2Einteger_2Eint__bijections,axiom,
( ! [V0a: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__ABS__CLASS @ ( mono_2Ec_2Einteger_2Eint__REP__CLASS @ V0a ) )
= V0a )
& ! [V1r: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ? [V2r: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V2r @ V2r )
& ( V1r
= ( mono_2Ec_2Einteger_2Etint__eq @ V2r ) ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__REP__CLASS @ ( mono_2Ec_2Einteger_2Eint__ABS__CLASS @ V1r ) )
= V1r ) ) ) ).
thf(thm_2Einteger_2Eint__REP__def,axiom,
! [V0a: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__REP @ V0a )
= ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( mono_2Ec_2Einteger_2Eint__REP__CLASS @ V0a ) ) ) ).
thf(thm_2Einteger_2Eint__ABS__def,axiom,
! [V0r: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Eint__ABS @ V0r )
= ( mono_2Ec_2Einteger_2Eint__ABS__CLASS @ ( mono_2Ec_2Einteger_2Etint__eq @ V0r ) ) ) ).
thf(thm_2Einteger_2Eint__0,axiom,
( mono_2Ec_2Einteger_2Eint__0
= ( mono_2Ec_2Einteger_2Eint__ABS @ mono_2Ec_2Einteger_2Etint__0 ) ) ).
thf(thm_2Einteger_2Eint__1,axiom,
( mono_2Ec_2Einteger_2Eint__1
= ( mono_2Ec_2Einteger_2Eint__ABS @ mono_2Ec_2Einteger_2Etint__1 ) ) ).
thf(thm_2Einteger_2Eint__neg,axiom,
! [V0T1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ V0T1 )
= ( mono_2Ec_2Einteger_2Eint__ABS @ ( mono_2Ec_2Einteger_2Etint__neg @ ( mono_2Ec_2Einteger_2Eint__REP @ V0T1 ) ) ) ) ).
thf(thm_2Einteger_2Eint__add,axiom,
! [V0T1: mono_2Etyop_2Einteger_2Eint,V1T2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V0T1 @ V1T2 )
= ( mono_2Ec_2Einteger_2Eint__ABS @ ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Einteger_2Eint__REP @ V0T1 ) @ ( mono_2Ec_2Einteger_2Eint__REP @ V1T2 ) ) ) ) ).
thf(thm_2Einteger_2Eint__mul,axiom,
! [V0T1: mono_2Etyop_2Einteger_2Eint,V1T2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V0T1 @ V1T2 )
= ( mono_2Ec_2Einteger_2Eint__ABS @ ( mono_2Ec_2Einteger_2Etint__mul @ ( mono_2Ec_2Einteger_2Eint__REP @ V0T1 ) @ ( mono_2Ec_2Einteger_2Eint__REP @ V1T2 ) ) ) ) ).
thf(thm_2Einteger_2Eint__lt,axiom,
! [V0T1: mono_2Etyop_2Einteger_2Eint,V1T2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0T1 @ V1T2 )
= ( mono_2Ec_2Einteger_2Etint__lt @ ( mono_2Ec_2Einteger_2Eint__REP @ V0T1 ) @ ( mono_2Ec_2Einteger_2Eint__REP @ V1T2 ) ) ) ).
thf(thm_2Einteger_2ENum,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0i: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0i @ V1n )
<=> ( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) )
=> ! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2ENum @ V0i )
= ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V0i ) ) ) ) ).
thf(thm_2Einteger_2Eint__div,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,F1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V0i @ V1j )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) @ ( mono_2Ec_2Einteger_2ENum @ V1j ) )
= mono_2Ec_2Enum_2E0 ) )
=> ( ! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( F1 @ V0i @ V1j )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Einteger_2ENum @ V0i ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V1j ) ) )
= mono_2Ec_2Enum_2E0 ) )
=> ! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1j
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ V0i @ V1j )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1j ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ V0i ) @ ( mono_2Ec_2Einteger_2ENum @ V1j ) ) ) @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) @ ( mono_2Ec_2Einteger_2ENum @ V1j ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F0 @ V0i @ V1j ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i ) @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ V0i ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V1j ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F1 @ V0i @ V1j ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V1j ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2Eint__mod,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1j
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V1j )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0i @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ V0i @ V1j ) @ V1j ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS,axiom,
! [V0n: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2EABS @ V0n )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ V0n @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V0n ) @ V0n ) ) ).
thf(thm_2Einteger_2Eint__quot,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1j
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ V0i @ V1j )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1j ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ V0i ) @ ( mono_2Ec_2Einteger_2ENum @ V1j ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) @ ( mono_2Ec_2Einteger_2ENum @ V1j ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ V0i ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V1j ) ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V0i ) ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__neg @ V1j ) ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2Eint__rem,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1j
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ V0i @ V1j )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0i @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__quot @ V0i @ V1j ) @ V1j ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
<=> ? [V2m: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V2m @ V0p )
= V1q ) ) ).
thf(thm_2Einteger_2Eint__exp,axiom,
( ! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__exp @ V0p @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ! [V1p: mono_2Etyop_2Einteger_2Eint,V2n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__exp @ V1p @ ( mono_2Ec_2Enum_2ESUC @ V2n ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ V1p @ ( mono_2Ec_2Einteger_2Eint__exp @ V1p @ V2n ) ) ) ) ).
thf(thm_2Einteger_2EINT__MIN,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__min @ V0x @ V1y )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y ) @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__MAX,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__max @ V0x @ V1y )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y ) @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2ELEAST__INT__DEF,axiom,
! [F0: ( mono_2Etyop_2Einteger_2Eint > $o ) > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V0P: mono_2Etyop_2Einteger_2Eint > $o,V1i: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V0P @ V1i )
<=> ( ( V0P @ V1i )
& ! [V2j: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V2j @ V1i )
=> ( (~) @ ( V0P @ V2j ) ) ) ) )
=> ! [V0P: mono_2Etyop_2Einteger_2Eint > $o] :
( ( mono_2Ec_2Einteger_2ELEAST__INT @ V0P )
= ( mono_2Ec_2Emin_2E_40_2Emono_2Etyop_2Einteger_2Eint @ ( F0 @ V0P ) ) ) ) ).
thf(thm_2Einteger_2EINT__LT,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0m @ V1n ) ) ).
thf(thm_2Einteger_2EINT__LE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0m @ V1n ) ) ).
thf(thm_2Einteger_2EINT__POS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) ).
thf(thm_2Einteger_2EINT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__RMUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z )
= ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V2z ) )
<=> ( ( V2z
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( V0x = V1y ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__LMUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) )
<=> ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( V1y = V2z ) ) ) ).
thf(thm_2Einteger_2EINT__ENTIRE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( V1y
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__LT__ADDL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LT__ADDR,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LE__ADDL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V1y @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LE__ADDR,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LT__IMP__NE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
=> ( (~) @ ( V0x = V1y ) ) ) ).
thf(thm_2Einteger_2EINT__NEG__MINUS1,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ V0x )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__NEG__EQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V0x )
= V1y )
<=> ( V0x
= ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__RDISTRIB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__LDISTRIB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__ADD__SUB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ V0x )
= V1y ) ).
thf(thm_2Einteger_2EINT__SUB__LE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__SUB__LT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__NEG__SUB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__NEG__0,axiom,
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__NEG__EQ0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V0x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__LE__NEGR,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__LE__NEGL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ V0x )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LE__DOUBLE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V0x ) )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__SUB__0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Einteger_2EINT__SUB__REFL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V0x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__SUB__ADD2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V1y @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= V0x ) ).
thf(thm_2Einteger_2EINT__SUB__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) @ V1y )
= V0x ) ).
thf(thm_2Einteger_2EINT__LT__ADD1,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
=> ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__LT__ADDNEG2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V2z @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__ADDNEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V2z ) ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V2z ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LT__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LE__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LE__ADD2,axiom,
! [V0w: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint,V2y: mono_2Etyop_2Einteger_2Eint,V3z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ V0w @ V1x )
& ( mono_2Ec_2Einteger_2Eint__le @ V2y @ V3z ) )
=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__add @ V0w @ V2y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V3z ) ) ) ).
thf(thm_2Einteger_2EINT__LT__ADD2,axiom,
! [V0w: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint,V2y: mono_2Etyop_2Einteger_2Eint,V3z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ V0w @ V1x )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2y @ V3z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0w @ V2y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V3z ) ) ) ).
thf(thm_2Einteger_2EINT__LE__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LE__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V2z ) ) ).
thf(thm_2Einteger_2EINT__LT__01,axiom,
mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Einteger_2EINT__LE__01,axiom,
mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ).
thf(thm_2Einteger_2EINT__LE__SQUARE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LE__MUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LE__NEGTOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
| ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__LT__NEGTOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__NEG__GE0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__NEG__LE0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__NEG__GT0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__NEG__LT0,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LTE__ANTSYM,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( (~)
@ ( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__LET__ANTISYM,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( (~)
@ ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__LE__ANTISYM,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Einteger_2EINT__LE__TRANS,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2EINT__LET__TRANS,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2EINT__LTE__TRANS,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2EINT__LT__IMP__LE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
=> ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LT__LE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
& ( (~) @ ( V0x = V1y ) ) ) ) ).
thf(thm_2Einteger_2EINT__LE__LT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
| ( V0x = V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LE__REFL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V0x ) ).
thf(thm_2Einteger_2EINT__LTE__TOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LET__TOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LE__TOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__NOT__LE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( (~) @ ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y ) )
<=> ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LT__GT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
=> ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__LT__ANTISYM,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( (~)
@ ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__NOT__LT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y ) )
<=> ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LT__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LT__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z ) ) ).
thf(thm_2Einteger_2EINT__NEG__MUL2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__NEGNEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) )
= V0x ) ).
thf(thm_2Einteger_2EINT__NEG__RMUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__NEG__LMUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ V1y ) ) ).
thf(thm_2Einteger_2EINT__MUL__RZERO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__MUL__LZERO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__NEG__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__RNEG__UNIQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V1y
= ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__LNEG__UNIQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V0x
= ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__ADD__RID__UNIQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y )
= V0x )
<=> ( V1y
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__ADD__LID__UNIQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y )
= V1y )
<=> ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z )
= ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V2z ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Einteger_2EINT__EQ__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) )
<=> ( V1y = V2z ) ) ).
thf(thm_2Einteger_2EINT__RDISTRIB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__RID,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= V0x ) ).
thf(thm_2Einteger_2EINT__MUL__LID,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V0x )
= V0x ) ).
thf(thm_2Einteger_2EINT__ADD__RINV,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__ADD__LINV,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ V0x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__ADD__RID,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2Einteger_2EINT__ADD__LID,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
= V0x ) ).
thf(thm_2Einteger_2EINT__1,axiom,
( mono_2Ec_2Einteger_2Eint__1
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ).
thf(thm_2Einteger_2EINT__0,axiom,
( mono_2Ec_2Einteger_2Eint__0
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2ENUM__POSINT__EX,axiom,
! [V0t: mono_2Etyop_2Einteger_2Eint] :
( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V0t @ mono_2Ec_2Einteger_2Eint__0 ) )
=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( V0t
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) ) ).
thf(thm_2Einteger_2EINT__LT__MUL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ mono_2Ec_2Einteger_2Eint__0 @ V0x )
& ( mono_2Ec_2Einteger_2Eint__lt @ mono_2Ec_2Einteger_2Eint__0 @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ mono_2Ec_2Einteger_2Eint__0 @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__LADD__IMP,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__LT__TRANS,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2EINT__LT__REFL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] : ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LT__TOTAL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( V0x = V1y )
| ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LDISTRIB,axiom,
! [V0z: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ V0z ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__ASSOC,axiom,
! [V0z: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V0z ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ V1y ) @ V0z ) ) ).
thf(thm_2Einteger_2EINT__ADD__ASSOC,axiom,
! [V0z: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V2x @ ( mono_2Ec_2Einteger_2Eint__add @ V1y @ V0z ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ V2x @ V1y ) @ V0z ) ) ).
thf(thm_2Einteger_2EINT__MUL__COMM,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0y @ V1x ) ) ).
thf(thm_2Einteger_2EINT__MUL__SYM,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0y @ V1x ) ) ).
thf(thm_2Einteger_2EINT__ADD__COMM,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__add @ V0y @ V1x ) ) ).
thf(thm_2Einteger_2EINT__ADD__SYM,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__add @ V0y @ V1x ) ) ).
thf(thm_2Einteger_2EINT__10,axiom,
(~) @ ( mono_2Ec_2Einteger_2Eint__1 = mono_2Ec_2Einteger_2Eint__0 ) ).
thf(thm_2Einteger_2EEQ__LADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n )
= ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V2p ) )
<=> ( V1n = V2p ) ) ).
thf(thm_2Einteger_2EEQ__ADDL,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( V0x
= ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V1y ) )
<=> ( V1y = mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2ELT__LADD,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum,V2z: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V1y ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V2z ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1y @ V2z ) ) ).
thf(thm_2Einteger_2ELT__ADDL,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V1y ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V1y ) ) ).
thf(thm_2Einteger_2ELT__ADDR,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x @ V1y ) @ V0x ) ) ).
thf(thm_2Einteger_2ELT__ADD2,axiom,
! [V0x1: mono_2Etyop_2Enum_2Enum,V1x2: mono_2Etyop_2Enum_2Enum,V2y1: mono_2Etyop_2Enum_2Enum,V3y2: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Eprim__rec_2E_3C @ V0x1 @ V2y1 )
& ( mono_2Ec_2Eprim__rec_2E_3C @ V1x2 @ V3y2 ) )
=> ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Earithmetic_2E_2B @ V0x1 @ V1x2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ V2y1 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2ETINT__EQ__REFL,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Einteger_2Etint__eq @ V0x @ V0x ) ).
thf(thm_2Einteger_2ETINT__EQ__SYM,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Etint__eq @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2ETINT__EQ__TRANS,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__eq @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Etint__eq @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Etint__eq @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2ETINT__EQ__EQUIV,axiom,
! [V0p: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1q: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0p @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Etint__eq @ V0p )
= ( mono_2Ec_2Einteger_2Etint__eq @ V1q ) ) ) ).
thf(thm_2Einteger_2ETINT__EQ__AP,axiom,
! [V0p: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1q: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( V0p = V1q )
=> ( mono_2Ec_2Einteger_2Etint__eq @ V0p @ V1q ) ) ).
thf(thm_2Einteger_2ETINT__10,axiom,
(~) @ ( mono_2Ec_2Einteger_2Etint__eq @ mono_2Ec_2Einteger_2Etint__1 @ mono_2Ec_2Einteger_2Etint__0 ) ).
thf(thm_2Einteger_2ETINT__ADD__SYM,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__add @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Etint__add @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2ETINT__MUL__SYM,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Etint__mul @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2ETINT__ADD__ASSOC,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__add @ V0x @ ( mono_2Ec_2Einteger_2Etint__add @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Einteger_2Etint__add @ V0x @ V1y ) @ V2z ) ) ).
thf(thm_2Einteger_2ETINT__MUL__ASSOC,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ ( mono_2Ec_2Einteger_2Etint__mul @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Etint__mul @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ V1y ) @ V2z ) ) ).
thf(thm_2Einteger_2ETINT__LDISTRIB,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ ( mono_2Ec_2Einteger_2Etint__add @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ V2z ) ) ) ).
thf(thm_2Einteger_2ETINT__ADD__LID,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__add @ mono_2Ec_2Einteger_2Etint__0 @ V0x ) @ V0x ) ).
thf(thm_2Einteger_2ETINT__MUL__LID,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__mul @ mono_2Ec_2Einteger_2Etint__1 @ V0x ) @ V0x ) ).
thf(thm_2Einteger_2ETINT__ADD__LINV,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__add @ ( mono_2Ec_2Einteger_2Etint__neg @ V0x ) @ V0x ) @ mono_2Ec_2Einteger_2Etint__0 ) ).
thf(thm_2Einteger_2ETINT__LT__TOTAL,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V1y )
| ( mono_2Ec_2Einteger_2Etint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2ETINT__LT__REFL,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] : ( (~) @ ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V0x ) ) ).
thf(thm_2Einteger_2ETINT__LT__TRANS,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Etint__lt @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2ETINT__LT__ADD,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2z: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__lt @ V1y @ V2z )
=> ( mono_2Ec_2Einteger_2Etint__lt @ ( mono_2Ec_2Einteger_2Etint__add @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Etint__add @ V0x @ V2z ) ) ) ).
thf(thm_2Einteger_2ETINT__LT__MUL,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__lt @ mono_2Ec_2Einteger_2Etint__0 @ V0x )
& ( mono_2Ec_2Einteger_2Etint__lt @ mono_2Ec_2Einteger_2Etint__0 @ V1y ) )
=> ( mono_2Ec_2Einteger_2Etint__lt @ mono_2Ec_2Einteger_2Etint__0 @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2ETINT__NEG__WELLDEF,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
=> ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__neg @ V0x1 ) @ ( mono_2Ec_2Einteger_2Etint__neg @ V1x2 ) ) ) ).
thf(thm_2Einteger_2ETINT__ADD__WELLDEFR,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
=> ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__add @ V0x1 @ V2y ) @ ( mono_2Ec_2Einteger_2Etint__add @ V1x2 @ V2y ) ) ) ).
thf(thm_2Einteger_2ETINT__ADD__WELLDEF,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V3y2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
& ( mono_2Ec_2Einteger_2Etint__eq @ V2y1 @ V3y2 ) )
=> ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__add @ V0x1 @ V2y1 ) @ ( mono_2Ec_2Einteger_2Etint__add @ V1x2 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2ETINT__MUL__WELLDEFR,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
=> ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x1 @ V2y ) @ ( mono_2Ec_2Einteger_2Etint__mul @ V1x2 @ V2y ) ) ) ).
thf(thm_2Einteger_2ETINT__MUL__WELLDEF,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V3y2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
& ( mono_2Ec_2Einteger_2Etint__eq @ V2y1 @ V3y2 ) )
=> ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__mul @ V0x1 @ V2y1 ) @ ( mono_2Ec_2Einteger_2Etint__mul @ V1x2 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2ETINT__LT__WELLDEFR,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
=> ( ( mono_2Ec_2Einteger_2Etint__lt @ V0x1 @ V2y )
= ( mono_2Ec_2Einteger_2Etint__lt @ V1x2 @ V2y ) ) ) ).
thf(thm_2Einteger_2ETINT__LT__WELLDEFL,axiom,
! [V0x: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V1y1 @ V2y2 )
=> ( ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V1y1 )
= ( mono_2Ec_2Einteger_2Etint__lt @ V0x @ V2y2 ) ) ) ).
thf(thm_2Einteger_2ETINT__LT__WELLDEF,axiom,
! [V0x1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V1x2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V2y1: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,V3y2: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( ( mono_2Ec_2Einteger_2Etint__eq @ V0x1 @ V1x2 )
& ( mono_2Ec_2Einteger_2Etint__eq @ V2y1 @ V3y2 ) )
=> ( ( mono_2Ec_2Einteger_2Etint__lt @ V0x1 @ V2y1 )
= ( mono_2Ec_2Einteger_2Etint__lt @ V1x2 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2Etint__of__num__eq,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2Etint__of__num @ V0n ) )
= ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Einteger_2Etint__of__num @ V0n ) ) @ V0n ) ) ).
thf(thm_2Einteger_2ETINT__INJ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Etint__eq @ ( mono_2Ec_2Einteger_2Etint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Etint__of__num @ V1n ) )
<=> ( V0m = V1n ) ) ).
thf(thm_2Einteger_2ENUM__POSTINT__EX,axiom,
! [V0t: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( (~) @ ( mono_2Ec_2Einteger_2Etint__lt @ V0t @ mono_2Ec_2Einteger_2Etint__0 ) )
=> ? [V1n: mono_2Etyop_2Enum_2Enum] : ( mono_2Ec_2Einteger_2Etint__eq @ V0t @ ( mono_2Ec_2Einteger_2Etint__of__num @ V1n ) ) ) ).
thf(thm_2Einteger_2Eint__ABS__REP__CLASS,axiom,
( ! [V0a: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__ABS__CLASS @ ( mono_2Ec_2Einteger_2Eint__REP__CLASS @ V0a ) )
= V0a )
& ! [V1c: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 > $o] :
( ? [V2r: mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29] :
( ( mono_2Ec_2Einteger_2Etint__eq @ V2r @ V2r )
& ( V1c
= ( mono_2Ec_2Einteger_2Etint__eq @ V2r ) ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__REP__CLASS @ ( mono_2Ec_2Einteger_2Eint__ABS__CLASS @ V1c ) )
= V1c ) ) ) ).
thf(thm_2Einteger_2Eint__QUOTIENT,axiom,
mono_2Ec_2Equotient_2EQUOTIENT_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Einteger_2Eint @ mono_2Ec_2Einteger_2Etint__eq @ mono_2Ec_2Einteger_2Eint__ABS @ mono_2Ec_2Einteger_2Eint__REP ).
thf(thm_2Einteger_2Eint__of__num,axiom,
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Einteger_2Eint__0 )
& ! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Enum_2ESUC @ V0n ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ mono_2Ec_2Einteger_2Eint__1 ) ) ) ).
thf(thm_2Einteger_2EINT__INJ,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V0m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
<=> ( V0m = V1n ) ) ).
thf(thm_2Einteger_2EINT__ADD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2B @ V0m @ V1n ) ) ) ).
thf(thm_2Einteger_2EINT__MUL,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ).
thf(thm_2Einteger_2EINT__LT__NZ,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( (~)
@ ( ( mono_2Ec_2Einteger_2Eint__of__num @ V0n )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
<=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__NZ__IMP__LT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__DOUBLE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V0x )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V0x ) ) ).
thf(thm_2Einteger_2EINT__SUB__SUB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) @ V0x )
= ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LT__ADD__SUB,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__sub @ V2z @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__SUB__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V2z @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__SUB__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LE__SUB__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z ) @ V1y ) ) ).
thf(thm_2Einteger_2EINT__LE__SUB__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) @ V2z )
= ( mono_2Ec_2Einteger_2Eint__le @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V2z @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__NEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__LE__NEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__ADD2__SUB2,axiom,
! [V0a: mono_2Etyop_2Einteger_2Eint,V1b: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint,V3d: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__add @ V0a @ V1b ) @ ( mono_2Ec_2Einteger_2Eint__add @ V2c @ V3d ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ V0a @ V2c ) @ ( mono_2Ec_2Einteger_2Eint__sub @ V1b @ V3d ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__LZERO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
= ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) ) ).
thf(thm_2Einteger_2EINT__SUB__RZERO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= V0x ) ).
thf(thm_2Einteger_2EINT__LET__ADD2,axiom,
! [V0w: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint,V2y: mono_2Etyop_2Einteger_2Eint,V3z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ V0w @ V1x )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2y @ V3z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0w @ V2y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V3z ) ) ) ).
thf(thm_2Einteger_2EINT__LTE__ADD2,axiom,
! [V0w: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint,V2y: mono_2Etyop_2Einteger_2Eint,V3z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ V0w @ V1x )
& ( mono_2Ec_2Einteger_2Eint__le @ V2y @ V3z ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__add @ V0w @ V2y ) @ ( mono_2Ec_2Einteger_2Eint__add @ V1x @ V3z ) ) ) ).
thf(thm_2Einteger_2EINT__LET__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LTE__ADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1y ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LT__MUL2,axiom,
! [V0x1: mono_2Etyop_2Einteger_2Eint,V1x2: mono_2Etyop_2Einteger_2Eint,V2y1: mono_2Etyop_2Einteger_2Eint,V3y2: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x1 )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V2y1 )
& ( mono_2Ec_2Einteger_2Eint__lt @ V0x1 @ V1x2 )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2y1 @ V3y2 ) )
=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x1 @ V2y1 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1x2 @ V3y2 ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__LNEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ V1y )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__RNEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__SUB__NEG2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__SUB__TRIANGLE,axiom,
! [V0a: mono_2Etyop_2Einteger_2Eint,V1b: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ V0a @ V1b ) @ ( mono_2Ec_2Einteger_2Eint__sub @ V1b @ V2c ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0a @ V2c ) ) ).
thf(thm_2Einteger_2EINT__EQ__SUB__LADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( V0x
= ( mono_2Ec_2Einteger_2Eint__sub @ V1y @ V2z ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V2z )
= V1y ) ) ).
thf(thm_2Einteger_2EINT__EQ__SUB__RADD,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
= V2z )
<=> ( V0x
= ( mono_2Ec_2Einteger_2Eint__add @ V2z @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__SUB,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n )
=> ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2D @ V0n @ V1m ) ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__SUB2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= V1y ) ).
thf(thm_2Einteger_2EINT__ADD__SUB2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ).
thf(thm_2Einteger_2EINT__EQ__LMUL2,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( V1y = V2z )
<=> ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__IMP__LE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( V0x = V1y )
=> ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y ) ) ).
thf(thm_2Einteger_2EINT__POS__NZ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
=> ( (~)
@ ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__RMUL__IMP,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V2z
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z )
= ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V2z ) ) )
=> ( V0x = V1y ) ) ).
thf(thm_2Einteger_2EINT__EQ__LMUL__IMP,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) ) )
=> ( V1y = V2z ) ) ).
thf(thm_2Einteger_2EINT__DIFFSQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__POASQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V0x ) )
<=> ( (~)
@ ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__SUMSQ,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1y @ V1y ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( V1y
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__NEG,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V0x )
= ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) )
<=> ( V0x = V1y ) ) ).
thf(thm_2Einteger_2EINT__LT__CALCULATE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
<=> ( ( (~) @ ( V0n = mono_2Ec_2Enum_2E0 ) )
| ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) )
= mono_2Ec_2Ebool_2EF ) ) ).
thf(thm_2Einteger_2ENUM__POSINT,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0i: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0i @ V1n )
<=> ( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) )
=> ! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i )
=> ( mono_2Ec_2Ebool_2E_3F_21_2Emono_2Etyop_2Enum_2Enum @ ( F0 @ V0i ) ) ) ) ).
thf(thm_2Einteger_2ENUM__POSINT__EXISTS,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i )
=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) ) ).
thf(thm_2Einteger_2ENUM__NEGINT__EXISTS,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
=> ? [V1n: mono_2Etyop_2Enum_2Enum] :
( V0i
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) ) ) ).
thf(thm_2Einteger_2EINT__NUM__CASES,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ? [V1n: mono_2Etyop_2Enum_2Enum] :
( ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
& ( (~) @ ( V1n = mono_2Ec_2Enum_2E0 ) ) )
| ? [V2n: mono_2Etyop_2Enum_2Enum] :
( ( V0p
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V2n ) ) )
& ( (~) @ ( V2n = mono_2Ec_2Enum_2E0 ) ) )
| ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__DISCRETE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( (~)
@ ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__LE__LT1,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1x @ ( mono_2Ec_2Einteger_2Eint__add @ V0y @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__LT__LE1,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V1x @ V0y )
= ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__add @ V1x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ V0y ) ) ).
thf(thm_2Einteger_2EINT__MUL__EQ__1,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ( V1y
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
| ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V1y
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2ENUM__OF__INT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) )
= V0n ) ).
thf(thm_2Einteger_2EINT__OF__NUM,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Einteger_2ENum @ V0i ) )
= V0i )
<=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i ) ) ).
thf(thm_2Einteger_2ELE__NUM__OF__INT,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ V1i )
=> ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ ( mono_2Ec_2Einteger_2ENum @ V1i ) ) ) ).
thf(thm_2Einteger_2ENUM__LT,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1x )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0y ) )
=> ( ( mono_2Ec_2Eprim__rec_2E_3C @ ( mono_2Ec_2Einteger_2ENum @ V1x ) @ ( mono_2Ec_2Einteger_2ENum @ V0y ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1x @ V0y ) ) ) ).
thf(thm_2Einteger_2EINT__DIV,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ V0n @ V1m ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__1,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__div @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= V0p ) ).
thf(thm_2Einteger_2EINT__DIV__0,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__ID,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ V0p @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__BOUNDS,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,F1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V1q: mono_2Etyop_2Einteger_2Eint,V0p: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V1q @ V0p )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( F1 @ V0p @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q ) @ V1q ) ) )
=> ! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( F0 @ V1q @ V0p ) @ ( F1 @ V0p @ V1q ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVISION,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,F1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V0q: mono_2Etyop_2Einteger_2Eint,V1p: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V0q @ V1p )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0q @ ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ! [V1p: mono_2Etyop_2Einteger_2Eint,V0q: mono_2Etyop_2Einteger_2Eint] :
( ( F1 @ V1p @ V0q )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q ) @ V0q ) ) )
=> ! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1p: mono_2Etyop_2Einteger_2Eint] :
( ( V1p
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ V1p @ V0q ) @ V0q ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q ) ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V0q @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( F0 @ V0q @ V1p ) @ ( F1 @ V1p @ V0q ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ V0n @ V1m ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__MUL__ID,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ V0p @ V1q ) @ V1q )
= V0p ) ) ).
thf(thm_2Einteger_2EINT__DIV__UNIQUE,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,F1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V1j: mono_2Etyop_2Einteger_2Eint,V3r: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V1j @ V3r )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V1j @ V3r )
& ( mono_2Ec_2Einteger_2Eint__le @ V3r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ! [V3r: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( F1 @ V3r @ V1j )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3r )
& ( mono_2Ec_2Einteger_2Eint__lt @ V3r @ V1j ) ) )
=> ! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint,V2q: mono_2Etyop_2Einteger_2Eint] :
( ? [V3r: mono_2Etyop_2Einteger_2Eint] :
( ( V0i
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V2q @ V1j ) @ V3r ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V1j @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( F0 @ V1j @ V3r ) @ ( F1 @ V3r @ V1j ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ V0i @ V1j )
= V2q ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__UNIQUE,axiom,
! [F0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o,F1: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o] :
( ! [V1j: mono_2Etyop_2Einteger_2Eint,V2m: mono_2Etyop_2Einteger_2Eint] :
( ( F0 @ V1j @ V2m )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V1j @ V2m )
& ( mono_2Ec_2Einteger_2Eint__le @ V2m @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ! [V2m: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( F1 @ V2m @ V1j )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V2m )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2m @ V1j ) ) )
=> ! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint,V2m: mono_2Etyop_2Einteger_2Eint] :
( ? [V3q: mono_2Etyop_2Einteger_2Eint] :
( ( V0i
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3q @ V1j ) @ V2m ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ V1j @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( F0 @ V1j @ V2m ) @ ( F1 @ V2m @ V1j ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V1j )
= V2m ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__ID,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V0i )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__COMMON__FACTOR,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__mul @ V1q @ V0p ) @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__LMUL,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__mul @ V0i @ V1j ) @ V0i )
= V1j ) ) ).
thf(thm_2Einteger_2EINT__DIV__RMUL,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0i
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__mul @ V1j @ V0i ) @ V0i )
= V1j ) ) ).
thf(thm_2Einteger_2EINT__MOD__EQ0,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mod @ V1p @ V0q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ? [V2k: mono_2Etyop_2Einteger_2Eint] :
( V1p
= ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ V0q ) ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__DIV,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2k: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0p @ V1q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ V0p ) @ V1q )
= ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ ( mono_2Ec_2Einteger_2Eint__div @ V0p @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__ADD__DIV,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint,V2k: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V2k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V2k )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( mono_2Ec_2Einteger_2Eint__mod @ V1j @ V2k )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__add @ V0i @ V1j ) @ V2k )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__div @ V0i @ V2k ) @ ( mono_2Ec_2Einteger_2Eint__div @ V1j @ V2k ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__ADD__MULTIPLES,axiom,
! [V0r: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2k: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V2k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V1q @ V2k ) @ V0r ) @ V2k )
= ( mono_2Ec_2Einteger_2Eint__mod @ V0r @ V2k ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__NEG__NUMERATOR,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1k: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ V1k )
= ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__sub @ V1k @ V0x ) @ V1k ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__PLUS,axiom,
! [V0k: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint,V2i: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mod @ V2i @ V0k ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V1j @ V0k ) ) @ V0k )
= ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__add @ V2i @ V1j ) @ V0k ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__SUB,axiom,
! [V0k: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint,V2i: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mod @ V2i @ V0k ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V1j @ V0k ) ) @ V0k )
= ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__sub @ V2i @ V1j ) @ V0k ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__MOD,axiom,
! [V0k: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0k
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__mod @ V1j @ V0k ) @ V0k )
= ( mono_2Ec_2Einteger_2Eint__mod @ V1j @ V0k ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__P,axiom,
! [V0P: mono_2Etyop_2Einteger_2Eint > $o,V1x: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V2c
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( V0P @ ( mono_2Ec_2Einteger_2Eint__div @ V1x @ V2c ) )
<=> ? [V3k: mono_2Etyop_2Einteger_2Eint,V4r: mono_2Etyop_2Einteger_2Eint] :
( ( V1x
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3k @ V2c ) @ V4r ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ V4r )
& ( mono_2Ec_2Einteger_2Eint__le @ V4r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V4r )
& ( mono_2Ec_2Einteger_2Eint__lt @ V4r @ V2c ) ) )
& ( V0P @ V3k ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__P,axiom,
! [V0P: mono_2Etyop_2Einteger_2Eint > $o,V1x: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V2c
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( V0P @ ( mono_2Ec_2Einteger_2Eint__mod @ V1x @ V2c ) )
<=> ? [V3k: mono_2Etyop_2Einteger_2Eint,V4r: mono_2Etyop_2Einteger_2Eint] :
( ( V1x
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3k @ V2c ) @ V4r ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ V4r )
& ( mono_2Ec_2Einteger_2Eint__le @ V4r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V4r )
& ( mono_2Ec_2Einteger_2Eint__lt @ V4r @ V2c ) ) )
& ( V0P @ V4r ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__FORALL__P,axiom,
! [V0P: mono_2Etyop_2Einteger_2Eint > $o,V1x: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V2c
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( V0P @ ( mono_2Ec_2Einteger_2Eint__div @ V1x @ V2c ) )
<=> ! [V3k: mono_2Etyop_2Einteger_2Eint,V4r: mono_2Etyop_2Einteger_2Eint] :
( ( ( V1x
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3k @ V2c ) @ V4r ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ V4r )
& ( mono_2Ec_2Einteger_2Eint__le @ V4r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V4r )
& ( mono_2Ec_2Einteger_2Eint__lt @ V4r @ V2c ) ) ) )
=> ( V0P @ V3k ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__FORALL__P,axiom,
! [V0P: mono_2Etyop_2Einteger_2Eint > $o,V1x: mono_2Etyop_2Einteger_2Eint,V2c: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V2c
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( V0P @ ( mono_2Ec_2Einteger_2Eint__mod @ V1x @ V2c ) )
<=> ! [V3q: mono_2Etyop_2Einteger_2Eint,V4r: mono_2Etyop_2Einteger_2Eint] :
( ( ( V1x
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3q @ V2c ) @ V4r ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ V4r )
& ( mono_2Ec_2Einteger_2Eint__le @ V4r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ V2c @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V4r )
& ( mono_2Ec_2Einteger_2Eint__lt @ V4r @ V2c ) ) ) )
=> ( V0P @ V4r ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__1,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Einteger_2EINT__LESS__MOD,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1j: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0i )
& ( mono_2Ec_2Einteger_2Eint__lt @ V0i @ V1j ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V1j )
= V0i ) ) ).
thf(thm_2Einteger_2EINT__MOD__MINUS1,axiom,
! [V0n: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0n )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ V0n )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0n @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__POS,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) ).
thf(thm_2Einteger_2EINT__ABS__NUM,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) ) ).
thf(thm_2Einteger_2EINT__NEG__SAME__EQ,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( V0p
= ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) )
<=> ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) )
= ( mono_2Ec_2Einteger_2EABS @ V0p ) ) ).
thf(thm_2Einteger_2EINT__ABS__ABS,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2EABS @ V0p ) )
= ( mono_2Ec_2Einteger_2EABS @ V0p ) ) ).
thf(thm_2Einteger_2EINT__ABS__EQ__ID,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2EABS @ V0p )
= V0p )
<=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p ) ) ).
thf(thm_2Einteger_2EINT__ABS__MUL,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2EABS @ V0p ) @ ( mono_2Ec_2Einteger_2EABS @ V1q ) )
= ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V1q ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__EQ0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2EABS @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__LT0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] : ( (~) @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2EABS @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__0LT,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2EABS @ V0p ) )
<=> ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__LE0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2EABS @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__LT,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2EABS @ V0p ) @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ V1q )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) @ V0p ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2EABS @ V0p ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ V0p )
| ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) @ V0p )
| ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ V1q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ V0p ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__LE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2EABS @ V0p ) @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ V0p @ V1q )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) @ V0p ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__le @ V1q @ ( mono_2Ec_2Einteger_2EABS @ V0p ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ V1q @ V0p )
| ( mono_2Ec_2Einteger_2Eint__le @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) @ V1q )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) @ V0p )
| ( mono_2Ec_2Einteger_2Eint__le @ V0p @ V1q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__le @ V1q @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) )
<=> ( ( mono_2Ec_2Einteger_2Eint__le @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__le @ V1q @ V0p ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__EQ,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( ( mono_2Ec_2Einteger_2EABS @ V0p )
= V1q )
<=> ( ( ( V0p = V1q )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) )
| ( ( V0p
= ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) ) ) )
& ( ( V1q
= ( mono_2Ec_2Einteger_2EABS @ V0p ) )
<=> ( ( ( V0p = V1q )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) )
| ( ( V0p
= ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__EQ__ABS,axiom,
! [V0y: mono_2Etyop_2Einteger_2Eint,V1x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2EABS @ V1x )
= ( mono_2Ec_2Einteger_2EABS @ V0y ) )
<=> ( ( V1x = V0y )
| ( V1x
= ( mono_2Ec_2Einteger_2Eint__neg @ V0y ) ) ) ) ).
thf(thm_2Einteger_2EINT__QUOT,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1q = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ V0p @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__QUOT__0,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__QUOT__1,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= V0p ) ).
thf(thm_2Einteger_2EINT__QUOT__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V1q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V1q ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__ABS__QUOT,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V1q ) @ V1q ) ) @ ( mono_2Ec_2Einteger_2EABS @ V0p ) ) ) ).
thf(thm_2Einteger_2EINT__QUOT__UNIQUE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2k: mono_2Etyop_2Einteger_2Eint] :
( ? [V3r: mono_2Etyop_2Einteger_2Eint] :
( ( V0p
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ V1q ) @ V3r ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3r ) @ ( mono_2Ec_2Einteger_2Eint__le @ V3r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2EABS @ V3r ) @ ( mono_2Ec_2Einteger_2EABS @ V1q ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V1q )
= V2k ) ) ).
thf(thm_2Einteger_2EINT__QUOT__ID,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__REM,axiom,
! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1q = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ V0p @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__REMQUOT,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1p: mono_2Etyop_2Einteger_2Eint] :
( ( V1p
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__quot @ V1p @ V0q ) @ V0q ) @ ( mono_2Ec_2Einteger_2Eint__rem @ V1p @ V0q ) ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1p ) @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__rem @ V1p @ V0q ) ) @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__rem @ V1p @ V0q ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Einteger_2Eint__rem @ V1p @ V0q ) ) @ ( mono_2Ec_2Einteger_2EABS @ V0q ) ) ) ) ).
thf(thm_2Einteger_2EINT__REM__UNIQUE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2EABS @ V2r ) @ ( mono_2Ec_2Einteger_2EABS @ V1q ) )
& ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V2r ) @ ( mono_2Ec_2Einteger_2Eint__le @ V2r @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ? [V3k: mono_2Etyop_2Einteger_2Eint] :
( V0p
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V3k @ V1q ) @ V2r ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ V1q )
= V2r ) ) ).
thf(thm_2Einteger_2EINT__REM__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ V1q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__REM__ID,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__REM0,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__REM__COMMON__FACTOR,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__mul @ V1q @ V0p ) @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__REM__EQ0,axiom,
! [V0q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ! [V1p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__rem @ V1p @ V0q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ? [V2k: mono_2Etyop_2Einteger_2Eint] :
( V1p
= ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ V0q ) ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__QUOT,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2k: mono_2Etyop_2Einteger_2Eint] :
( ( ( (~)
@ ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ V0p @ V1q )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ V0p ) @ V1q )
= ( mono_2Ec_2Einteger_2Eint__mul @ V2k @ ( mono_2Ec_2Einteger_2Eint__quot @ V0p @ V1q ) ) ) ) ).
thf(thm_2Einteger_2EINT__REM__EQ__MOD,axiom,
! [V0i: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1n )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ V0i @ V1n )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__lt @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__sub @ V0i @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ V1n ) @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__mod @ V0i @ V1n ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__MOD0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
<=> ( ( ( ( mono_2Ec_2Einteger_2Eint__mod @ V1q @ V0p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
| ( ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( V1q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__0,axiom,
( ! [V0x: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ! [V1x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1x )
<=> ( V1x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__1,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ V0x )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V0x
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
| ( V0x
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__REFL,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint] : ( mono_2Ec_2Einteger_2Eint__divides @ V0x @ V0x ) ).
thf(thm_2Einteger_2EINT__DIVIDES__TRANS,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__divides @ V1y @ V2z ) )
=> ( mono_2Ec_2Einteger_2Eint__divides @ V0x @ V2z ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__MUL,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V1q ) )
& ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__mul @ V1q @ V0p ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__LMUL,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__mul @ V1q @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__RMUL,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__mul @ V2r @ V1q ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__MUL__BOTH,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V1q ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V2r ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V1q @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__LADD,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__add @ V1q @ V2r ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__RADD,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__add @ V2r @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__NEG,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__neg @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) @ V1q )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__LSUB,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__sub @ V1q @ V2r ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__RSUB,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint,V2r: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V1q )
=> ( ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ ( mono_2Ec_2Einteger_2Eint__sub @ V2r @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__divides @ V0p @ V2r ) ) ) ).
thf(thm_2Einteger_2EINT__EXP,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ V1m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ V1m ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__EQ0,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__exp @ V0p @ V1n )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( ( V0p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( (~) @ ( V1n = mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__SIGN__CASES,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1q: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V1q ) )
<=> ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) )
| ( ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mul @ V0p @ V1q ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1q @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
| ( ( mono_2Ec_2Einteger_2Eint__lt @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1q ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__NEG,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Earithmetic_2EEVEN @ V0n )
=> ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) @ V0n )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ V0n ) ) ) )
& ( ( mono_2Ec_2Earithmetic_2EODD @ V0n )
=> ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) ) @ V0n )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EEXP @ V1m @ V0n ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__ADD__EXPONENTS,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V0n @ V1m ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__MULTIPLY__EXPONENTS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V1n ) @ V0m )
= ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ ( mono_2Ec_2Earithmetic_2E_2A @ V1n @ V0m ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__MOD,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m )
& ( (~)
@ ( V2p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__SUBTRACT__EXPONENTS,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V0m )
& ( (~)
@ ( V2p
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ ( mono_2Ec_2Earithmetic_2E_2D @ V0m @ V1n ) ) ) ) ).
thf(thm_2Einteger_2EINT__MIN__LT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ ( mono_2Ec_2Einteger_2Eint__min @ V1y @ V2z ) )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
& ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__MAX__LT,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__max @ V0x @ V1y ) @ V2z )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V2z )
& ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__MIN__NUM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__min @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMIN @ V0m @ V1n ) ) ) ).
thf(thm_2Einteger_2EINT__MAX__NUM,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__max @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMAX @ V0m @ V1n ) ) ) ).
thf(thm_2Einteger_2EINT__LT__MONO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V2z ) ) ) ).
thf(thm_2Einteger_2EINT__LE__MONO,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint,V2z: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0x )
=> ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V1y ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V0x @ V2z ) )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V2z ) ) ) ).
thf(thm_2Einteger_2EINFINITE__INT__UNIV,axiom,
(~) @ ( mono_2Ec_2Epred__set_2EFINITE_2Emono_2Etyop_2Einteger_2Eint @ mono_2Ec_2Epred__set_2EUNIV_2Emono_2Etyop_2Einteger_2Eint ) ).
thf(thm_2Einteger_2EINT__ADD__CALCULATE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p )
= V0p )
& ( ( mono_2Ec_2Einteger_2Eint__add @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= V0p )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V2m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2m ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V2m ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V2m ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V1n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2m ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V2m ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2m ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__ADD__REDUCE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V0p )
= V0p )
& ( ( mono_2Ec_2Einteger_2Eint__add @ V0p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= V0p )
& ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V0p ) )
= V0p )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V2m ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Enumeral_2EiZ @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2m ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V2m ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V2m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V2m ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1n @ V2m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2D @ V2m @ V1n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2D @ V1n @ V2m ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V2m ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Enumeral_2EiZ @ ( mono_2Ec_2Earithmetic_2E_2B @ V1n @ V2m ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__CALCULATE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__add @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ V1y ) ) ) ).
thf(thm_2Einteger_2EINT__SUB__REDUCE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__sub @ V2p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= V2p )
& ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V2p )
= ( mono_2Ec_2Einteger_2Eint__neg @ V2p ) )
& ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__MUL__CALCULATE,axiom,
( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0m ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) )
& ! [V2x: mono_2Etyop_2Einteger_2Eint,V3y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ V2x ) @ V3y )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ V2x @ V3y ) ) )
& ! [V4x: mono_2Etyop_2Einteger_2Eint,V5y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__mul @ V4x @ ( mono_2Ec_2Einteger_2Eint__neg @ V5y ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mul @ V4x @ V5y ) ) )
& ! [V6x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V6x ) )
= V6x ) ) ).
thf(thm_2Einteger_2EINT__MUL__REDUCE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__mul @ V2p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V2p )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2E_2A @ V0m @ V1n ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__DIV__CALCULATE,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ V0n @ V1m ) ) ) )
& ! [V2p: mono_2Etyop_2Einteger_2Eint,V3q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V3q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__div @ V2p @ ( mono_2Ec_2Einteger_2Eint__neg @ V3q ) )
= ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ V2p ) @ V3q ) ) )
& ! [V4m: mono_2Etyop_2Enum_2Enum,V5n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V4m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V5n ) )
<=> ( V4m = V5n ) )
& ! [V6x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V6x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V6x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ! [V7x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V7x ) )
= V7x ) ) ).
thf(thm_2Einteger_2EINT__DIV__REDUCE,axiom,
! [F3: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,F1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,F2: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,F0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F3 @ V0m @ V1n )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) )
= mono_2Ec_2Enum_2E0 ) )
=> ( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F1 @ V0m @ V1n )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) )
= mono_2Ec_2Enum_2E0 ) )
=> ( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F2 @ V0m @ V1n )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) )
= mono_2Ec_2Enum_2E0 ) )
=> ( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V0m @ V1n )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) )
= mono_2Ec_2Enum_2E0 ) )
=> ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F0 @ V0m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F1 @ V0m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F2 @ V0m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Einteger_2Eint @ ( F3 @ V0m @ V1n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__QUOT__CALCULATE,axiom,
( ! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1q = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ V0p @ V1q ) ) ) )
& ! [V2p: mono_2Etyop_2Einteger_2Eint,V3q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V3q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ V2p ) @ V3q )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__quot @ V2p @ V3q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ V2p @ ( mono_2Ec_2Einteger_2Eint__neg @ V3q ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__quot @ V2p @ V3q ) ) ) ) )
& ! [V4m: mono_2Etyop_2Enum_2Enum,V5n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V4m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V5n ) )
<=> ( V4m = V5n ) )
& ! [V6x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V6x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V6x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
& ! [V7x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V7x ) )
= V7x ) ) ).
thf(thm_2Einteger_2EINT__QUOT__REDUCE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__quot @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EDIV @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__CALCULATE,axiom,
( ! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1m = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0n ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ V0n @ V1m ) ) ) )
& ! [V2p: mono_2Etyop_2Einteger_2Eint,V3q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V3q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2Eint__mod @ V2p @ ( mono_2Ec_2Einteger_2Eint__neg @ V3q ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ V2p ) @ V3q ) ) ) )
& ! [V4x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V4x ) )
= V4x )
& ! [V5m: mono_2Etyop_2Enum_2Enum,V6n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V5m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V6n ) )
<=> ( V5m = V6n ) )
& ! [V7x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V7x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V7x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__MOD__REDUCE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1m: mono_2Etyop_2Enum_2Enum,V2n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__mod @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__sub @ V0x @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ V0x @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2n ) ) ) ) @ V0x ) )
& ( ( mono_2Ec_2Einteger_2Eint__mod @ V0x @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__div @ ( mono_2Ec_2Einteger_2Eint__neg @ V0x ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2n ) ) ) ) @ V0x ) ) ) ).
thf(thm_2Einteger_2EINT__REM__CALCULATE,axiom,
( ! [V0p: mono_2Etyop_2Enum_2Enum,V1q: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V1q = mono_2Ec_2Enum_2E0 ) )
=> ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ V0p ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1q ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ V0p @ V1q ) ) ) )
& ! [V2p: mono_2Etyop_2Einteger_2Eint,V3q: mono_2Etyop_2Einteger_2Eint] :
( ( (~)
@ ( V3q
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ V2p ) @ V3q )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__rem @ V2p @ V3q ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ V2p @ ( mono_2Ec_2Einteger_2Eint__neg @ V3q ) )
= ( mono_2Ec_2Einteger_2Eint__rem @ V2p @ V3q ) ) ) )
& ! [V4x: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__neg @ V4x ) )
= V4x )
& ! [V5m: mono_2Etyop_2Enum_2Enum,V6n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V5m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V6n ) )
<=> ( V5m = V6n ) )
& ! [V7x: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V7x )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> ( V7x
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ) ).
thf(thm_2Einteger_2EINT__REM__REDUCE,axiom,
! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1n ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__rem @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1n ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__CALCULATE,axiom,
! [V0p: mono_2Etyop_2Einteger_2Eint,V1n: mono_2Etyop_2Enum_2Enum,V2m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__exp @ V0p @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) @ V2m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ V2m ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2m ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V2m ) ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2m ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EEXP @ V1n @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V2m ) ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EXP__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__exp @ V2p @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ V1m ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1m ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1m ) ) ) ) ) )
& ( ( mono_2Ec_2Einteger_2Eint__exp @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1m ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EEXP @ V0n @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1m ) ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__LT__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__LE__CALCULATE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__le @ V0x @ V1y )
<=> ( ( mono_2Ec_2Einteger_2Eint__lt @ V0x @ V1y )
| ( V0x = V1y ) ) ) ).
thf(thm_2Einteger_2EINT__LE__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m ) )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1m ) ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1m ) ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__le @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__GT__CALCULATE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__gt @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__lt @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__GT__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V0n @ V1m ) )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__gt @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) )
= ( mono_2Ec_2Eprim__rec_2E_3C @ V1m @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__GE__CALCULATE,axiom,
! [V0x: mono_2Etyop_2Einteger_2Eint,V1y: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__ge @ V0x @ V1y )
= ( mono_2Ec_2Einteger_2Eint__le @ V1y @ V0x ) ) ).
thf(thm_2Einteger_2EINT__GE__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V0n @ V1m ) )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V1m ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V1m ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__ge @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) ) )
= ( mono_2Ec_2Earithmetic_2E_3C_3D @ V1m @ V0n ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__CALCULATE,axiom,
( ! [V0m: mono_2Etyop_2Enum_2Enum,V1n: mono_2Etyop_2Enum_2Enum] :
( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V0m )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V1n ) )
<=> ( V0m = V1n ) )
& ! [V2x: mono_2Etyop_2Einteger_2Eint,V3y: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__neg @ V2x )
= ( mono_2Ec_2Einteger_2Eint__neg @ V3y ) )
<=> ( V2x = V3y ) )
& ! [V4n: mono_2Etyop_2Enum_2Enum,V5m: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ V4n )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V5m ) ) )
<=> ( ( V4n = mono_2Ec_2Enum_2E0 )
& ( V5m = mono_2Ec_2Enum_2E0 ) ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ V4n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ V5m ) )
<=> ( ( V4n = mono_2Ec_2Enum_2E0 )
& ( V5m = mono_2Ec_2Enum_2E0 ) ) ) ) ) ).
thf(thm_2Einteger_2EINT__EQ__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum] :
( ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> mono_2Ec_2Ebool_2ET )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> ( V0n = V1m ) )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> mono_2Ec_2Ebool_2EF )
& ( ( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V0n ) ) )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> ( V0n = V1m ) ) ) ).
thf(thm_2Einteger_2EINT__DIVIDES__REDUCE,axiom,
! [V0n: mono_2Etyop_2Enum_2Enum,V1m: mono_2Etyop_2Enum_2Enum,V2p: mono_2Etyop_2Einteger_2Eint] :
( ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) )
= mono_2Ec_2Ebool_2EF )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ V2p @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
= mono_2Ec_2Ebool_2ET )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) )
& ( ( mono_2Ec_2Einteger_2Eint__divides @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) ) ) @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) ) ) )
<=> ( ( mono_2Ec_2Earithmetic_2EMOD @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ V1m ) @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT2 @ V0n ) ) )
= mono_2Ec_2Enum_2E0 ) ) ) ).
%------------------------------------------------------------------------------