ITP001 Axioms: ITP123^4.ax
%------------------------------------------------------------------------------
% File : ITP123^4 : 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 : frac.ax [Gau19]
% : HL4123^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 439 ( 177 unt; 232 typ; 0 def)
% Number of atoms : 304 ( 219 equ; 13 cnn)
% Maximal formula atoms : 8 ( 0 avg)
% Number of connectives : 2460 ( 13 ~; 6 |; 7 &;2387 @)
% ( 16 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg;2387 nst)
% Number of types : 8 ( 7 usr)
% Number of type conns : 495 ( 495 >; 0 *; 0 +; 0 <<)
% Number of symbols : 227 ( 225 usr; 59 con; 0-3 aty)
% Number of variables : 336 ( 0 ^ 334 !; 2 ?; 336 :)
% 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_2Efrac_2Efrac,type,
mono_2Etyop_2Efrac_2Efrac: $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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: $tType ).
thf(tyop_2Efrac_2Efrac,type,
tyop_2Efrac_2Efrac: d ).
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_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: u ).
thf(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: du > du > u ).
thf(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: u ).
thf(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0: u ).
thf(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2: du > du > u ).
thf(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: u ).
thf(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: du > du > u ).
thf(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0: u ).
thf(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1: du > u ).
thf(c_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_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: 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_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_2Ebool_2EONE__ONE_2E0,type,
c_2Ebool_2EONE__ONE_2E0: u ).
thf(c_2Ebool_2EONE__ONE_2E1,type,
c_2Ebool_2EONE__ONE_2E1: du > u ).
thf(c_2Ebool_2EONTO_2E0,type,
c_2Ebool_2EONTO_2E0: u ).
thf(c_2Ebool_2EONTO_2E1,type,
c_2Ebool_2EONTO_2E1: du > u ).
thf(c_2EintExtension_2ESGN_2E0,type,
c_2EintExtension_2ESGN_2E0: u ).
thf(c_2EintExtension_2ESGN_2E1,type,
c_2EintExtension_2ESGN_2E1: 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_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0: u ).
thf(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2: du > du > u ).
thf(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: u ).
thf(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: du > du > u ).
thf(c_2Efrac_2Eabs__frac_2E0,type,
c_2Efrac_2Eabs__frac_2E0: u ).
thf(c_2Efrac_2Eabs__frac_2E1,type,
c_2Efrac_2Eabs__frac_2E1: du > u ).
thf(c_2Efrac_2Efrac__0_2E0,type,
c_2Efrac_2Efrac__0_2E0: u ).
thf(c_2Efrac_2Efrac__1_2E0,type,
c_2Efrac_2Efrac__1_2E0: u ).
thf(c_2Efrac_2Efrac__add_2E0,type,
c_2Efrac_2Efrac__add_2E0: u ).
thf(c_2Efrac_2Efrac__add_2E2,type,
c_2Efrac_2Efrac__add_2E2: du > du > u ).
thf(c_2Efrac_2Efrac__ainv_2E0,type,
c_2Efrac_2Efrac__ainv_2E0: u ).
thf(c_2Efrac_2Efrac__ainv_2E1,type,
c_2Efrac_2Efrac__ainv_2E1: du > u ).
thf(c_2Efrac_2Efrac__div_2E0,type,
c_2Efrac_2Efrac__div_2E0: u ).
thf(c_2Efrac_2Efrac__div_2E2,type,
c_2Efrac_2Efrac__div_2E2: du > du > u ).
thf(c_2Efrac_2Efrac__dnm_2E0,type,
c_2Efrac_2Efrac__dnm_2E0: u ).
thf(c_2Efrac_2Efrac__dnm_2E1,type,
c_2Efrac_2Efrac__dnm_2E1: du > u ).
thf(c_2Efrac_2Efrac__minv_2E0,type,
c_2Efrac_2Efrac__minv_2E0: u ).
thf(c_2Efrac_2Efrac__minv_2E1,type,
c_2Efrac_2Efrac__minv_2E1: du > u ).
thf(c_2Efrac_2Efrac__mul_2E0,type,
c_2Efrac_2Efrac__mul_2E0: u ).
thf(c_2Efrac_2Efrac__mul_2E2,type,
c_2Efrac_2Efrac__mul_2E2: du > du > u ).
thf(c_2Efrac_2Efrac__nmr_2E0,type,
c_2Efrac_2Efrac__nmr_2E0: u ).
thf(c_2Efrac_2Efrac__nmr_2E1,type,
c_2Efrac_2Efrac__nmr_2E1: du > u ).
thf(c_2Efrac_2Efrac__save_2E0,type,
c_2Efrac_2Efrac__save_2E0: u ).
thf(c_2Efrac_2Efrac__save_2E2,type,
c_2Efrac_2Efrac__save_2E2: du > du > u ).
thf(c_2Efrac_2Efrac__sgn_2E0,type,
c_2Efrac_2Efrac__sgn_2E0: u ).
thf(c_2Efrac_2Efrac__sgn_2E1,type,
c_2Efrac_2Efrac__sgn_2E1: du > u ).
thf(c_2Efrac_2Efrac__sub_2E0,type,
c_2Efrac_2Efrac__sub_2E0: u ).
thf(c_2Efrac_2Efrac__sub_2E2,type,
c_2Efrac_2Efrac__sub_2E2: du > 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__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__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__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_2Efrac_2Eles__abs_2E0,type,
c_2Efrac_2Eles__abs_2E0: u ).
thf(c_2Efrac_2Eles__abs_2E2,type,
c_2Efrac_2Eles__abs_2E2: du > du > u ).
thf(c_2Efrac_2Erep__frac_2E0,type,
c_2Efrac_2Erep__frac_2E0: u ).
thf(c_2Efrac_2Erep__frac_2E1,type,
c_2Efrac_2Erep__frac_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_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Efrac_2Efrac > $o ) > mono_2Etyop_2Efrac_2Efrac > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o ) > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
mono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o ) > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ).
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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
mono_2Eapp_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ).
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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Einteger_2Eint: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ) > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ).
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_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_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_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ).
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_2Ebool_2EONE__ONE_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ).
thf(mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ).
thf(mono_2Ec_2EintExtension_2ESGN,type,
mono_2Ec_2EintExtension_2ESGN: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,type,
mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,type,
mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $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_2Efrac_2Eabs__frac,type,
mono_2Ec_2Efrac_2Eabs__frac: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__0,type,
mono_2Ec_2Efrac_2Efrac__0: mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__1,type,
mono_2Ec_2Efrac_2Efrac__1: mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__add,type,
mono_2Ec_2Efrac_2Efrac__add: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__ainv,type,
mono_2Ec_2Efrac_2Efrac__ainv: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__div,type,
mono_2Ec_2Efrac_2Efrac__div: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__dnm,type,
mono_2Ec_2Efrac_2Efrac__dnm: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Efrac_2Efrac__minv,type,
mono_2Ec_2Efrac_2Efrac__minv: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__mul,type,
mono_2Ec_2Efrac_2Efrac__mul: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__nmr,type,
mono_2Ec_2Efrac_2Efrac__nmr: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Efrac_2Efrac__save,type,
mono_2Ec_2Efrac_2Efrac__save: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ).
thf(mono_2Ec_2Efrac_2Efrac__sgn,type,
mono_2Ec_2Efrac_2Efrac__sgn: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Efrac_2Efrac__sub,type,
mono_2Ec_2Efrac_2Efrac__sub: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
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__lt,type,
mono_2Ec_2Einteger_2Eint__lt: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > $o ).
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__sub,type,
mono_2Ec_2Einteger_2Eint__sub: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint ).
thf(mono_2Ec_2Efrac_2Eles__abs,type,
mono_2Ec_2Efrac_2Eles__abs: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o ).
thf(mono_2Ec_2Efrac_2Erep__frac,type,
mono_2Ec_2Efrac_2Erep__frac: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Efrac_2Efrac,type,
i_mono_2Etyop_2Efrac_2Efrac: mono_2Etyop_2Efrac_2Efrac > 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_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Efrac_2Efrac > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ) > 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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: ( mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ) > 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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ) > 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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Efrac_2Efrac,type,
j_mono_2Etyop_2Efrac_2Efrac: du > mono_2Etyop_2Efrac_2Efrac ).
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_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Efrac_2Efrac > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29: du > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29: du > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ).
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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29: du > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac ).
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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint ).
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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,type,
j_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29: du > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Efrac_2Efrac,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ ( j_mono_2Etyop_2Efrac_2Efrac @ ( s @ tyop_2Efrac_2Efrac @ V0_2E0 ) ) ) )
= ( s @ tyop_2Efrac_2Efrac @ 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_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ 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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) ) @ 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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ 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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Efrac_2Efrac ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Efrac_2Efrac ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ 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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ 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_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Efrac_2Efrac @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ 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_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( j_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > $o,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Efrac_2Efrac @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V0 ) ) @ ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o,V1: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( 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_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o,V1: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_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_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_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_2Enum_2Enum_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Efrac_2Efrac @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Efrac_2Efrac_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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( s @ tyop_2Efrac_2Efrac @ ( i_mono_2Etyop_2Efrac_2Efrac @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Efrac_2Efrac @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_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_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E0_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Emin_2Efun_28tyop_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_29 @ mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Emin_2Efun @ tyop_2Einteger_2Eint @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) ) @ c_2Epair_2E_2C_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Einteger_2Eint] :
( ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0 @ V1 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V0 ) ) @ ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E0_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ c_2Epair_2EFST_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Epair_2EFST_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONE__ONE_2E0_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EONE__ONE_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONE__ONE_2E1_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EONE__ONE_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONTO_2E0_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_2Ctyop_2Emin_2Ebool_29 @ mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2EONTO_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2EONTO_2E1_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac @ V0 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2EONTO_2E1 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ tyop_2Efrac_2Efrac ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E0_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Einteger_2Eint_29 @ mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Einteger_2Eint ) @ c_2Epair_2ESND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( s @ tyop_2Einteger_2Eint @ ( i_mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0 ) ) )
= ( s @ tyop_2Einteger_2Eint @ ( c_2Epair_2ESND_2E1 @ ( s @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ ( i_mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 @ V0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E0_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,axiom,
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29_29 @ mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ tyop_2Emin_2Ebool ) ) @ c_2Ebool_2ETYPE__DEFINITION_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o,V1: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac @ V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ETYPE__DEFINITION_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Efrac_2Efrac @ ( tyop_2Epair_2Eprod @ tyop_2Einteger_2Eint @ tyop_2Einteger_2Eint ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29 @ V1 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > $o,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > $o,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Efrac_2Efrac_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac ) > $o,V1: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Efrac_2Efrac] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o,V1: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Efrac_2Efrac_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o ) > ( mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 ) > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o] :
( ( 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_2Einteger_2Eint_2Ctyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,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_2Efrac_2Efrac_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac,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_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,axiom,
! [V0: mono_2Etyop_2Einteger_2Eint > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29,V1: mono_2Etyop_2Einteger_2Eint] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Efrac_2Efrac,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_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_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Efrac_2Efrac,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Einteger_2Eint,axiom,
! [V0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > mono_2Etyop_2Einteger_2Eint,V1: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2Efrac_2Efrac__TY__DEF,axiom,
! [F0: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29 > $o] :
( ! [V1f: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( F0 @ V1f )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V1f ) ) )
=> ? [V0rep: mono_2Etyop_2Efrac_2Efrac > mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] : ( mono_2Ec_2Ebool_2ETYPE__DEFINITION_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29_20mono_2Etyop_2Efrac_2Efrac @ F0 @ V0rep ) ) ).
thf(thm_2Efrac_2Efrac__tybij,axiom,
( ! [V0a: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Efrac_2Erep__frac @ V0a ) )
= V0a )
& ! [V1r: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V1r ) )
<=> ( ( mono_2Ec_2Efrac_2Erep__frac @ ( mono_2Ec_2Efrac_2Eabs__frac @ V1r ) )
= V1r ) ) ) ).
thf(thm_2Efrac_2Efrac__nmr__def,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f )
= ( mono_2Ec_2Epair_2EFST_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Efrac_2Erep__frac @ V0f ) ) ) ).
thf(thm_2Efrac_2Efrac__dnm__def,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f )
= ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Efrac_2Erep__frac @ V0f ) ) ) ).
thf(thm_2Efrac_2Efrac__sgn__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2EintExtension_2ESGN @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) ) ) ).
thf(thm_2Efrac_2Efrac__ainv__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f1 )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) ) ) ) ).
thf(thm_2Efrac_2Efrac__minv__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__minv @ V0f1 )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) ) @ ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) ) ) ) ) ).
thf(thm_2Efrac_2Efrac__0__def,axiom,
( mono_2Ec_2Efrac_2Efrac__0
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( 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_2Efrac_2Efrac__1__def,axiom,
( mono_2Ec_2Efrac_2Efrac__1
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( 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_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Efrac_2Eles__abs__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Eles__abs @ V0f1 @ V1f2 )
= ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V1f2 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V1f2 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) ) ) ) ).
thf(thm_2Efrac_2Efrac__add__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__add @ V0f1 @ V1f2 )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V1f2 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V1f2 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V1f2 ) ) ) ) ) ).
thf(thm_2Efrac_2Efrac__sub__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sub @ V0f1 @ V1f2 )
= ( mono_2Ec_2Efrac_2Efrac__add @ V0f1 @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V1f2 ) ) ) ).
thf(thm_2Efrac_2Efrac__mul__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ V1f2 )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V1f2 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V1f2 ) ) ) ) ) ).
thf(thm_2Efrac_2Efrac__div__def,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__div @ V0f1 @ V1f2 )
= ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ ( mono_2Ec_2Efrac_2Efrac__minv @ V1f2 ) ) ) ).
thf(thm_2Efrac_2Efrac__save__def,axiom,
! [V0nmr: mono_2Etyop_2Einteger_2Eint,V1dnm: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__save @ V0nmr @ V1dnm )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0nmr @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1dnm ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ).
thf(thm_2Efrac_2Efrac__bij,axiom,
( ! [V0a: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Efrac_2Erep__frac @ V0a ) )
= V0a )
& ! [V1r: mono_2Etyop_2Epair_2Eprod_28tyop_2Einteger_2Eint_2Ctyop_2Einteger_2Eint_29] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Epair_2ESND_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V1r ) )
<=> ( ( mono_2Ec_2Efrac_2Erep__frac @ ( mono_2Ec_2Efrac_2Eabs__frac @ V1r ) )
= V1r ) ) ) ).
thf(thm_2Efrac_2EFRAC,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f ) ) )
= V0f ) ).
thf(thm_2Efrac_2EFRAC__EQ,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
<=> ( ( V0a1 = V2a2 )
& ( V1b1 = V3b2 ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__EQ__ALT,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( V0f1 = V1f2 )
<=> ( ( ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 )
= ( mono_2Ec_2Efrac_2Efrac__nmr @ V1f2 ) )
& ( ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f1 )
= ( mono_2Ec_2Efrac_2Efrac__dnm @ V1f2 ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__NOT__EQ,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( (~)
@ ( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) ) )
<=> ( ( (~) @ ( V0a1 = V2a2 ) )
| ( (~) @ ( V1b1 = V3b2 ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__NOT__EQ__IMP,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( (~)
@ ( ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 )
= ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
=> ( (~)
@ ( ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__DNMPOS,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] : ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Efrac_2Efrac__dnm @ V0f ) ) ).
thf(thm_2Efrac_2ENMR,axiom,
! [V0a: mono_2Etyop_2Einteger_2Eint,V1b: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b )
=> ( ( mono_2Ec_2Efrac_2Efrac__nmr @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a @ V1b ) ) )
= V0a ) ) ).
thf(thm_2Efrac_2EDNM,axiom,
! [V0a: mono_2Etyop_2Einteger_2Eint,V1b: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b )
=> ( ( mono_2Ec_2Efrac_2Efrac__dnm @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a @ V1b ) ) )
= V1b ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__neg @ V0a1 ) @ V1b1 ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__MINV__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( (~)
@ ( V0a1
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Efrac_2Efrac__minv @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2EintExtension_2ESGN @ V0a1 ) @ V1b1 ) @ ( mono_2Ec_2Einteger_2EABS @ V0a1 ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Efrac_2Efrac__sgn @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) )
= ( mono_2Ec_2EintExtension_2ESGN @ V0a1 ) ) ) ).
thf(thm_2Efrac_2EFRAC__ADD__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( mono_2Ec_2Efrac_2Efrac__add @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ V3b2 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V2a2 @ V1b1 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1b1 @ V3b2 ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SUB__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( mono_2Ec_2Efrac_2Efrac__sub @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ V3b2 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V2a2 @ V1b1 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1b1 @ V3b2 ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__MULT__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( mono_2Ec_2Efrac_2Efrac__mul @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ V2a2 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1b1 @ V3b2 ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__DIV__CALCULATE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Einteger_2Eint,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Einteger_2Eint] :
( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V1b1 )
=> ( ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ V3b2 )
=> ( ( (~)
@ ( V2a2
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Efrac_2Efrac__div @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V0a1 @ V1b1 ) ) @ ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ V2a2 @ V3b2 ) ) )
= ( mono_2Ec_2Efrac_2Eabs__frac @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Einteger_2Eint_20mono_2Etyop_2Einteger_2Eint @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ ( mono_2Ec_2EintExtension_2ESGN @ V2a2 ) ) @ V3b2 ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V1b1 @ ( mono_2Ec_2Einteger_2EABS @ V2a2 ) ) ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__ADD__ASSOC,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac,V2c: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__add @ V0a @ ( mono_2Ec_2Efrac_2Efrac__add @ V1b @ V2c ) )
= ( mono_2Ec_2Efrac_2Efrac__add @ ( mono_2Ec_2Efrac_2Efrac__add @ V0a @ V1b ) @ V2c ) ) ).
thf(thm_2Efrac_2EFRAC__MUL__ASSOC,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac,V2c: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__mul @ V0a @ ( mono_2Ec_2Efrac_2Efrac__mul @ V1b @ V2c ) )
= ( mono_2Ec_2Efrac_2Efrac__mul @ ( mono_2Ec_2Efrac_2Efrac__mul @ V0a @ V1b ) @ V2c ) ) ).
thf(thm_2Efrac_2EFRAC__ADD__COMM,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__add @ V0a @ V1b )
= ( mono_2Ec_2Efrac_2Efrac__add @ V1b @ V0a ) ) ).
thf(thm_2Efrac_2EFRAC__MUL__COMM,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__mul @ V0a @ V1b )
= ( mono_2Ec_2Efrac_2Efrac__mul @ V1b @ V0a ) ) ).
thf(thm_2Efrac_2EFRAC__ADD__RID,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__add @ V0a @ mono_2Ec_2Efrac_2Efrac__0 )
= V0a ) ).
thf(thm_2Efrac_2EFRAC__MUL__RID,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__mul @ V0a @ mono_2Ec_2Efrac_2Efrac__1 )
= V0a ) ).
thf(thm_2Efrac_2EFRAC__1__0,axiom,
(~) @ ( mono_2Ec_2Efrac_2Efrac__1 = mono_2Ec_2Efrac_2Efrac__0 ) ).
thf(thm_2Efrac_2EFRAC__AINV__0,axiom,
( ( mono_2Ec_2Efrac_2Efrac__ainv @ mono_2Ec_2Efrac_2Efrac__0 )
= mono_2Ec_2Efrac_2Efrac__0 ) ).
thf(thm_2Efrac_2EFRAC__AINV__AINV,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f1 ) )
= V0f1 ) ).
thf(thm_2Efrac_2EFRAC__AINV__ADD,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__add @ V0f1 @ V1f2 ) )
= ( mono_2Ec_2Efrac_2Efrac__add @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V1f2 ) ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__SUB,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__sub @ V1f2 @ V0f1 ) )
= ( mono_2Ec_2Efrac_2Efrac__sub @ V0f1 @ V1f2 ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__RMUL,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ V1f2 ) )
= ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V1f2 ) ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__LMUL,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ V1f2 ) )
= ( mono_2Ec_2Efrac_2Efrac__mul @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f1 ) @ V1f2 ) ) ).
thf(thm_2Efrac_2EFRAC__MINV__1,axiom,
( ( mono_2Ec_2Efrac_2Efrac__minv @ mono_2Ec_2Efrac_2Efrac__1 )
= mono_2Ec_2Efrac_2Efrac__1 ) ).
thf(thm_2Efrac_2EFRAC__SUB__ADD,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac,V2c: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sub @ V0a @ ( mono_2Ec_2Efrac_2Efrac__add @ V1b @ V2c ) )
= ( mono_2Ec_2Efrac_2Efrac__sub @ ( mono_2Ec_2Efrac_2Efrac__sub @ V0a @ V1b ) @ V2c ) ) ).
thf(thm_2Efrac_2EFRAC__SUB__SUB,axiom,
! [V0a: mono_2Etyop_2Efrac_2Efrac,V1b: mono_2Etyop_2Efrac_2Efrac,V2c: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sub @ V0a @ ( mono_2Ec_2Efrac_2Efrac__sub @ V1b @ V2c ) )
= ( mono_2Ec_2Efrac_2Efrac__add @ ( mono_2Ec_2Efrac_2Efrac__sub @ V0a @ V1b ) @ V2c ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__TOTAL,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( 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_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__POS,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__NOT__NEG,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( (~)
@ ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( 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_2Enum_2E0 )
= ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) )
| ( mono_2Ec_2Einteger_2Eint__lt @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__NEG,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Efrac_2Efrac__sgn @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f ) ) )
= ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__IMP__EQGT,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( (~)
@ ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( 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_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
| ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__MUL,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sgn @ ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ V1f2 ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V1f2 ) ) ) ).
thf(thm_2Efrac_2EFRAC__ABS__SGN,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac] :
( ( (~)
@ ( ( mono_2Ec_2Efrac_2Efrac__nmr @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Einteger_2EABS @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 ) )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__MUL2,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1f2: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Efrac_2Efrac__sgn @ ( mono_2Ec_2Efrac_2Efrac__mul @ V0f1 @ V1f2 ) )
= ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 ) @ ( mono_2Ec_2Efrac_2Efrac__sgn @ V1f2 ) ) ) ).
thf(thm_2Efrac_2EFRAC__SGN__CASES,axiom,
! [V0f1: mono_2Etyop_2Efrac_2Efrac,V1P: $o] :
( ( ( ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
=> V1P )
& ( ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) )
=> V1P )
& ( ( ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f1 )
= ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
=> V1P ) )
=> V1P ) ).
thf(thm_2Efrac_2EFRAC__SGN__AINV,axiom,
! [V0f: mono_2Etyop_2Efrac_2Efrac] :
( ( mono_2Ec_2Einteger_2Eint__neg @ ( mono_2Ec_2Efrac_2Efrac__sgn @ ( mono_2Ec_2Efrac_2Efrac__ainv @ V0f ) ) )
= ( mono_2Ec_2Efrac_2Efrac__sgn @ V0f ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__ONEONE,axiom,
mono_2Ec_2Ebool_2EONE__ONE_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac @ mono_2Ec_2Efrac_2Efrac__ainv ).
thf(thm_2Efrac_2EFRAC__AINV__ONTO,axiom,
mono_2Ec_2Ebool_2EONTO_2Emono_2Etyop_2Efrac_2Efrac_20mono_2Etyop_2Efrac_2Efrac @ mono_2Ec_2Efrac_2Efrac__ainv ).
thf(thm_2Efrac_2EFRAC__NMR__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__nmr @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) )
= V0a1 ) ).
thf(thm_2Efrac_2EFRAC__DNM__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__dnm @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1b1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__0__SAVE,axiom,
( mono_2Ec_2Efrac_2Efrac__0
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Efrac_2EFRAC__1__SAVE,axiom,
( mono_2Ec_2Efrac_2Efrac__1
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) @ mono_2Ec_2Enum_2E0 ) ) ).
thf(thm_2Efrac_2EFRAC__AINV__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__ainv @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__neg @ V0a1 ) @ V1b1 ) ) ).
thf(thm_2Efrac_2EFRAC__MINV__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum] :
( ( (~)
@ ( V0a1
= ( mono_2Ec_2Einteger_2Eint__of__num @ mono_2Ec_2Enum_2E0 ) ) )
=> ( ( mono_2Ec_2Efrac_2Efrac__minv @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) )
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__mul @ ( mono_2Ec_2EintExtension_2ESGN @ V0a1 ) @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1b1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) @ ( mono_2Ec_2Einteger_2ENum @ ( mono_2Ec_2Einteger_2Eint__sub @ ( mono_2Ec_2Einteger_2EABS @ V0a1 ) @ ( mono_2Ec_2Einteger_2Eint__of__num @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ).
thf(thm_2Efrac_2EFRAC__ADD__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__add @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) @ ( mono_2Ec_2Efrac_2Efrac__save @ V2a2 @ V3b2 ) )
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__add @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ ( mono_2Ec_2Einteger_2Eint__of__num @ V3b2 ) ) @ ( mono_2Ec_2Einteger_2Eint__mul @ V2a2 @ ( mono_2Ec_2Einteger_2Eint__of__num @ V1b1 ) ) ) @ V0a1 ) @ V2a2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V1b1 @ V3b2 ) @ V1b1 ) @ V3b2 ) ) ) ).
thf(thm_2Efrac_2EFRAC__MUL__SAVE,axiom,
! [V0a1: mono_2Etyop_2Einteger_2Eint,V1b1: mono_2Etyop_2Enum_2Enum,V2a2: mono_2Etyop_2Einteger_2Eint,V3b2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Efrac_2Efrac__mul @ ( mono_2Ec_2Efrac_2Efrac__save @ V0a1 @ V1b1 ) @ ( mono_2Ec_2Efrac_2Efrac__save @ V2a2 @ V3b2 ) )
= ( mono_2Ec_2Efrac_2Efrac__save @ ( mono_2Ec_2Einteger_2Eint__mul @ V0a1 @ V2a2 ) @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2E_2A @ V1b1 @ V3b2 ) @ V1b1 ) @ V3b2 ) ) ) ).
%------------------------------------------------------------------------------