ITP001 Axioms: ITP080^4.ax
%------------------------------------------------------------------------------
% File : ITP080^4 : 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 : Omega_Automata.ax [Gau19]
% : HL4080^4.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 278 ( 71 unt; 163 typ; 0 def)
% Number of atoms : 674 ( 163 equ; 176 cnn)
% Maximal formula atoms : 66 ( 2 avg)
% Number of connectives : 12247 ( 176 ~; 98 |; 530 &;11251 @)
% ( 145 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 12 avg;11251 nst)
% Number of types : 5 ( 4 usr)
% Number of type conns : 524 ( 524 >; 0 *; 0 +; 0 <<)
% Number of symbols : 161 ( 159 usr; 48 con; 0-4 aty)
% Number of variables : 848 ( 0 ^ 631 !; 217 ?; 848 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(u,type,
u: $tType ).
thf(d,type,
d: $tType ).
thf(du,type,
du: $tType ).
thf(mono_2Etyop_2Enum_2Enum,type,
mono_2Etyop_2Enum_2Enum: $tType ).
thf(tyop_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_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_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: u ).
thf(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: du > du > u ).
thf(c_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_2ETemporal__Logic_2EALWAYS_2E0,type,
c_2ETemporal__Logic_2EALWAYS_2E0: u ).
thf(c_2ETemporal__Logic_2EALWAYS_2E1,type,
c_2ETemporal__Logic_2EALWAYS_2E1: du > u ).
thf(c_2ETemporal__Logic_2EBEFORE_2E0,type,
c_2ETemporal__Logic_2EBEFORE_2E0: u ).
thf(c_2ETemporal__Logic_2EBEFORE_2E2,type,
c_2ETemporal__Logic_2EBEFORE_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2EBEFORE_2E3,type,
c_2ETemporal__Logic_2EBEFORE_2E3: du > du > 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_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0: u ).
thf(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3: du > du > du > u ).
thf(c_2ETemporal__Logic_2EEVENTUAL_2E0,type,
c_2ETemporal__Logic_2EEVENTUAL_2E0: u ).
thf(c_2ETemporal__Logic_2EEVENTUAL_2E1,type,
c_2ETemporal__Logic_2EEVENTUAL_2E1: du > u ).
thf(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: u ).
thf(c_2Earithmetic_2EMOD_2E0,type,
c_2Earithmetic_2EMOD_2E0: u ).
thf(c_2Earithmetic_2EMOD_2E2,type,
c_2Earithmetic_2EMOD_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2ENEXT_2E0,type,
c_2ETemporal__Logic_2ENEXT_2E0: u ).
thf(c_2ETemporal__Logic_2ENEXT_2E1,type,
c_2ETemporal__Logic_2ENEXT_2E1: du > u ).
thf(c_2ETemporal__Logic_2ENEXT_2E2,type,
c_2ETemporal__Logic_2ENEXT_2E2: du > du > u ).
thf(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: u ).
thf(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: du > u ).
thf(c_2EPast__Temporal__Logic_2EPALWAYS_2E0,type,
c_2EPast__Temporal__Logic_2EPALWAYS_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPALWAYS_2E1,type,
c_2EPast__Temporal__Logic_2EPALWAYS_2E1: du > u ).
thf(c_2EPast__Temporal__Logic_2EPBEFORE_2E0,type,
c_2EPast__Temporal__Logic_2EPBEFORE_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPBEFORE_2E2,type,
c_2EPast__Temporal__Logic_2EPBEFORE_2E2: du > du > u ).
thf(c_2EPast__Temporal__Logic_2EPEVENTUAL_2E0,type,
c_2EPast__Temporal__Logic_2EPEVENTUAL_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1,type,
c_2EPast__Temporal__Logic_2EPEVENTUAL_2E1: du > u ).
thf(c_2EPast__Temporal__Logic_2EPNEXT_2E0,type,
c_2EPast__Temporal__Logic_2EPNEXT_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPNEXT_2E1,type,
c_2EPast__Temporal__Logic_2EPNEXT_2E1: du > u ).
thf(c_2EPast__Temporal__Logic_2EPSBEFORE_2E0,type,
c_2EPast__Temporal__Logic_2EPSBEFORE_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPSBEFORE_2E2,type,
c_2EPast__Temporal__Logic_2EPSBEFORE_2E2: du > du > u ).
thf(c_2EPast__Temporal__Logic_2EPSNEXT_2E0,type,
c_2EPast__Temporal__Logic_2EPSNEXT_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPSNEXT_2E1,type,
c_2EPast__Temporal__Logic_2EPSNEXT_2E1: du > u ).
thf(c_2EPast__Temporal__Logic_2EPSUNTIL_2E0,type,
c_2EPast__Temporal__Logic_2EPSUNTIL_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPSUNTIL_2E2,type,
c_2EPast__Temporal__Logic_2EPSUNTIL_2E2: du > du > u ).
thf(c_2EPast__Temporal__Logic_2EPSWHEN_2E0,type,
c_2EPast__Temporal__Logic_2EPSWHEN_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPSWHEN_2E2,type,
c_2EPast__Temporal__Logic_2EPSWHEN_2E2: du > du > u ).
thf(c_2EPast__Temporal__Logic_2EPUNTIL_2E0,type,
c_2EPast__Temporal__Logic_2EPUNTIL_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPUNTIL_2E2,type,
c_2EPast__Temporal__Logic_2EPUNTIL_2E2: du > du > u ).
thf(c_2EPast__Temporal__Logic_2EPWHEN_2E0,type,
c_2EPast__Temporal__Logic_2EPWHEN_2E0: u ).
thf(c_2EPast__Temporal__Logic_2EPWHEN_2E2,type,
c_2EPast__Temporal__Logic_2EPWHEN_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2ESBEFORE_2E0,type,
c_2ETemporal__Logic_2ESBEFORE_2E0: u ).
thf(c_2ETemporal__Logic_2ESBEFORE_2E2,type,
c_2ETemporal__Logic_2ESBEFORE_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2ESBEFORE_2E3,type,
c_2ETemporal__Logic_2ESBEFORE_2E3: du > du > du > u ).
thf(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: u ).
thf(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: du > u ).
thf(c_2ETemporal__Logic_2ESUNTIL_2E0,type,
c_2ETemporal__Logic_2ESUNTIL_2E0: u ).
thf(c_2ETemporal__Logic_2ESUNTIL_2E2,type,
c_2ETemporal__Logic_2ESUNTIL_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2ESUNTIL_2E3,type,
c_2ETemporal__Logic_2ESUNTIL_2E3: du > du > du > u ).
thf(c_2ETemporal__Logic_2ESWHEN_2E0,type,
c_2ETemporal__Logic_2ESWHEN_2E0: u ).
thf(c_2ETemporal__Logic_2ESWHEN_2E2,type,
c_2ETemporal__Logic_2ESWHEN_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2ESWHEN_2E3,type,
c_2ETemporal__Logic_2ESWHEN_2E3: du > du > du > u ).
thf(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: u ).
thf(c_2ETemporal__Logic_2EUNTIL_2E0,type,
c_2ETemporal__Logic_2EUNTIL_2E0: u ).
thf(c_2ETemporal__Logic_2EUNTIL_2E2,type,
c_2ETemporal__Logic_2EUNTIL_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2EUNTIL_2E3,type,
c_2ETemporal__Logic_2EUNTIL_2E3: du > du > du > u ).
thf(c_2ETemporal__Logic_2EWHEN_2E0,type,
c_2ETemporal__Logic_2EWHEN_2E0: u ).
thf(c_2ETemporal__Logic_2EWHEN_2E2,type,
c_2ETemporal__Logic_2EWHEN_2E2: du > du > u ).
thf(c_2ETemporal__Logic_2EWHEN_2E3,type,
c_2ETemporal__Logic_2EWHEN_2E3: du > 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_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: u ).
thf(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: du > u ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool: ( $o > $o ) > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o > $o ) > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o > $o ) > $o > $o > $o > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
mono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,type,
mono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Earithmetic_2E_2B,type,
mono_2Ec_2Earithmetic_2E_2B: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_2F_5C,type,
mono_2Ec_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(mono_2Ec_2Enum_2E0,type,
mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Eprim__rec_2E_3C,type,
mono_2Ec_2Eprim__rec_2E_3C: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Emin_2E_3D_3D_3E,type,
mono_2Ec_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(mono_2Ec_2ETemporal__Logic_2EALWAYS,type,
mono_2Ec_2ETemporal__Logic_2EALWAYS: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2ETemporal__Logic_2EBEFORE,type,
mono_2Ec_2ETemporal__Logic_2EBEFORE: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EBIT1,type,
mono_2Ec_2Earithmetic_2EBIT1: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool,type,
mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool: $o > $o > $o > $o ).
thf(mono_2Ec_2ETemporal__Logic_2EEVENTUAL,type,
mono_2Ec_2ETemporal__Logic_2EEVENTUAL: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2EF,type,
mono_2Ec_2Ebool_2EF: $o ).
thf(mono_2Ec_2Earithmetic_2EMOD,type,
mono_2Ec_2Earithmetic_2EMOD: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2ETemporal__Logic_2ENEXT,type,
mono_2Ec_2ETemporal__Logic_2ENEXT: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2ENUMERAL,type,
mono_2Ec_2Earithmetic_2ENUMERAL: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPALWAYS,type,
mono_2Ec_2EPast__Temporal__Logic_2EPALWAYS: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPBEFORE,type,
mono_2Ec_2EPast__Temporal__Logic_2EPBEFORE: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPEVENTUAL,type,
mono_2Ec_2EPast__Temporal__Logic_2EPEVENTUAL: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPNEXT,type,
mono_2Ec_2EPast__Temporal__Logic_2EPNEXT: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPSBEFORE,type,
mono_2Ec_2EPast__Temporal__Logic_2EPSBEFORE: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT,type,
mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPSUNTIL,type,
mono_2Ec_2EPast__Temporal__Logic_2EPSUNTIL: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPSWHEN,type,
mono_2Ec_2EPast__Temporal__Logic_2EPSWHEN: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPUNTIL,type,
mono_2Ec_2EPast__Temporal__Logic_2EPUNTIL: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2EPast__Temporal__Logic_2EPWHEN,type,
mono_2Ec_2EPast__Temporal__Logic_2EPWHEN: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2ETemporal__Logic_2ESBEFORE,type,
mono_2Ec_2ETemporal__Logic_2ESBEFORE: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Enum_2ESUC,type,
mono_2Ec_2Enum_2ESUC: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2ETemporal__Logic_2ESUNTIL,type,
mono_2Ec_2ETemporal__Logic_2ESUNTIL: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2ETemporal__Logic_2ESWHEN,type,
mono_2Ec_2ETemporal__Logic_2ESWHEN: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Ebool_2ET,type,
mono_2Ec_2Ebool_2ET: $o ).
thf(mono_2Ec_2ETemporal__Logic_2EUNTIL,type,
mono_2Ec_2ETemporal__Logic_2EUNTIL: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2ETemporal__Logic_2EWHEN,type,
mono_2Ec_2ETemporal__Logic_2EWHEN: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(mono_2Ec_2Earithmetic_2EZERO,type,
mono_2Ec_2Earithmetic_2EZERO: mono_2Etyop_2Enum_2Enum ).
thf(mono_2Ec_2Ebool_2E_5C_2F,type,
mono_2Ec_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(mono_2Ec_2Ebool_2E_7E,type,
mono_2Ec_2Ebool_2E_7E: $o > $o ).
thf(i_mono_2Etyop_2Emin_2Ebool,type,
i_mono_2Etyop_2Emin_2Ebool: $o > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: ( $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: ( $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: ( $o > $o > $o > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: ( ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: ( mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: ( mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ) > u ).
thf(i_mono_2Etyop_2Enum_2Enum,type,
i_mono_2Etyop_2Enum_2Enum: mono_2Etyop_2Enum_2Enum > u ).
thf(j_mono_2Etyop_2Emin_2Ebool,type,
j_mono_2Etyop_2Emin_2Ebool: du > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29: du > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29: du > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29: du > $o > $o > $o > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29: du > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29: du > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,type,
j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29: du > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum ).
thf(j_mono_2Etyop_2Enum_2Enum,type,
j_mono_2Etyop_2Enum_2Enum: du > mono_2Etyop_2Enum_2Enum ).
thf(reserved_2Eho_2Eeq__ext,axiom,
! [A_27a: d,A_27b: d,V0f_2E0: u,V1g_2E0: u] :
( ! [V2x_2E0: u] :
( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) )
=> ( ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V0f_2E0 )
= ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) ).
thf(reserved_2Eho_2Ei__thm,axiom,
! [A_27a: d,V0x_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27a ) @ combin_i_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Ek__thm,axiom,
! [A_27a: d,A_27b: d,V0x_2E0: u,V1y_2E0: u] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27a ) ) @ combin_k_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) @ ( s @ A_27b @ V1y_2E0 ) ) )
= ( s @ A_27a @ V0x_2E0 ) ) ).
thf(reserved_2Eho_2Es__thm,axiom,
! [A_27a: d,A_27b: d,A_27c: d,V0f_2E0: u,V1g_2E0: u,V2x_2E0: u] :
( ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ ( tyop_2Emin_2Efun @ A_27a @ A_27c ) ) ) @ combin_s_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) ) ) @ ( s @ A_27a @ V2x_2E0 ) ) )
= ( s @ A_27c @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ A_27c ) ) @ V0f_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ A_27b ) @ V1g_2E0 ) @ ( s @ A_27a @ V2x_2E0 ) ) ) ) ) ) ).
thf(reserved_2Elogic_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(reserved_2Elogic_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(reserved_2Elogic_2E_7E,axiom,
! [V0: $o] :
( ( mono_2Ec_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(reserved_2Elogic_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( mono_2Ec_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(reserved_2Elogic_2E_3D,axiom,
! [A_27a: d,V0_2E0: u,V1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Emin_2E_3D_2E2 @ ( s @ A_27a @ V0_2E0 ) @ ( s @ A_27a @ V1_2E0 ) ) ) )
<=> ( ( s @ A_27a @ V0_2E0 )
= ( s @ A_27a @ V1_2E0 ) ) ) ).
thf(reserved_2Equant_2E_21,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ! [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(reserved_2Equant_2E_3F,axiom,
! [A_27a: d,V0f_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) ) ) )
<=> ? [V1x_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V0f_2E0 ) @ ( s @ A_27a @ V1x_2E0 ) ) ) ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ) )
= ( s @ tyop_2Emin_2Ebool @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0_2E0: u] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ V0_2E0 ) ) ).
thf(ij_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0_2E0: u] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ) )
= ( s @ tyop_2Enum_2Enum @ V0_2E0 ) ) ).
thf(ji_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: $o > $o > $o > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) )
= V0 ) ).
thf(ji_2Emono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Enum_2Enum @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0 ) ) )
= V0 ) ).
thf(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_21_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_21_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b1,axiom,
! [A_27a: d,A_27b1: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b1 @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b1 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b1 @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2EA_27b2,axiom,
! [A_27a: d,A_27b2: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ A_27b2 @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27b2 @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27b2 @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28A_27state_2CA_27state_29,axiom,
! [A_27a: d,A_27state: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ X0_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27input_20mono_2EA_27state,axiom,
! [A_27input: d,A_27state: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27input @ X0_2E0 ) @ ( s @ A_27state @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27input @ ( tyop_2Emin_2Efun @ A_27state @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27input @ X0_2E0 ) ) ) @ ( s @ A_27state @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2EA_27state_20mono_2EA_27state,axiom,
! [A_27state: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ X0_2E0 ) @ ( s @ A_27state @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ ( tyop_2Emin_2Efun @ A_27state @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ A_27state @ X0_2E0 ) ) ) @ ( s @ A_27state @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b1_29,axiom,
! [A_27a: d,A_27b1: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b2_29,axiom,
! [A_27a: d,A_27b2: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27b_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: d,A_27b: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27input_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2CA_27state_29,axiom,
! [A_27input: d,A_27state: d,X0_2E0: u,X1_2E0: u] :
( ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ X0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ X1_2E0 ) ) )
= ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) ) @ c_2Epair_2E_2C_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ X0_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ X1_2E0 ) ) ) ) ).
thf(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u,X1_2E0: u] :
( ( ( s @ A_27a @ X0_2E0 )
= ( s @ A_27a @ X1_2E0 ) )
<=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ c_2Emin_2E_3D_2E0 ) @ ( s @ A_27a @ X0_2E0 ) ) ) @ ( s @ A_27a @ X1_2E0 ) ) ) ) ) ).
thf(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: d,X0_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2E_3F_2E1 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ c_2Ebool_2E_3F_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ X0_2E0 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o > $o,V1: $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29_29 @ V0 ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ ( V0 @ V1 ) ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Eapp_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( V0 @ V1 ) ) )
= ( s @ tyop_2Enum_2Enum @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Enum_2Enum ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29 @ V0 ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V1 ) ) ) ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E0_2Emono_2Etyop_2Emin_2Ebool,axiom,
( ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ ( i_mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29_29 @ mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool ) )
= ( s @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ ( tyop_2Emin_2Efun @ tyop_2Emin_2Ebool @ tyop_2Emin_2Ebool ) ) ) @ c_2Ebool_2ECOND_2E0 ) ) ).
thf(monoeq_2Emono_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o,V1: $o,V2: $o] :
( ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ V0 @ V1 @ V2 ) ) )
= ( s @ tyop_2Emin_2Ebool @ ( c_2Ebool_2ECOND_2E3 @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V0 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V1 ) ) @ ( s @ tyop_2Emin_2Ebool @ ( i_mono_2Etyop_2Emin_2Ebool @ V2 ) ) ) ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Ebool_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Efun_28tyop_2Emin_2Ebool_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: $o > $o > $o > $o,V1: $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [V0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum > $o] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Ebool,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(monoapp_2Emono_2Eapp_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [V0: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum,V1: mono_2Etyop_2Enum_2Enum] :
( ( V0 @ V1 )
= ( V0 @ V1 ) ) ).
thf(thm_2EOmega__Automata_2EDET__OMEGA__EXISTS__FORALL__THEOREM,axiom,
! [A_27input: d,A_27state: d,F1_2E0: u,F0_2E0: u] :
( ! [V8q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V10t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10t ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) )
=> ( ! [V5q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V7t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2TransRel_2E0: u,V3InitVal_2E0: u,V4Accept_2E0: u] :
( ? [V5q_2E0: u] :
( ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27state @ V3InitVal_2E0 ) )
& ! [V6t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) @ V2TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27input @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V4Accept_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) )
<=> ! [V8q_2E0: u] :
( ( ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27state @ V3InitVal_2E0 ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) @ V2TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27input @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) ) ) ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V4Accept_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ENEG__DET__AUTOMATA,axiom,
! [A_27input: d,A_27state: d,F1_2E0: u,F0_2E0: u] :
( ! [V8q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V10t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V10t ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) )
=> ( ! [V5q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V7t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2TransRel_2E0: u,V3InitVal_2E0: u,V4Accept_2E0: u] :
( ( (~)
@ ? [V5q_2E0: u] :
( ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27state @ V3InitVal_2E0 ) )
& ! [V6t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) @ V2TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27input @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V4Accept_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V5q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) ) )
<=> ? [V8q_2E0: u] :
( ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27state @ V3InitVal_2E0 ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ A_27state ) @ V2TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27input @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( (~) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V4Accept_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27input ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V8q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EOMEGA__CONJ__CLOSURE,axiom,
! [A_27a: d,A_27b1: d,A_27b2: d,V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2Psi2_2E0: u,V3Psi1_2E0: u,V4Phi__R2_2E0: u,V5Phi__R1_2E0: u,V6Phi__I2_2E0: u,V7Phi__I1_2E0: u] :
( ( ? [V8q1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) ) ) ) ) ) )
& ? [V10q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V11t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) ) ) ) ) ) ) )
<=> ? [V12q1_2E0: u,V13q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V12q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V14t: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V12q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V12q1_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EOMEGA__DISJ__CLOSURE,axiom,
! [A_27a: d,A_27b1: d,A_27b2: d,V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2Psi2_2E0: u,V3Psi1_2E0: u,V4Phi__R2_2E0: u,V5Phi__R1_2E0: u,V6Phi__I2_2E0: u,V7Phi__I1_2E0: u] :
( ( ? [V8q1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) ) ) ) ) ) )
| ? [V10q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V11t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V10q2_2E0 ) ) ) ) ) ) ) )
<=> ? [V12p: mono_2Etyop_2Enum_2Enum > $o,V13q1_2E0: u,V14q2_2E0: u] :
( ( ( ( (~) @ ( V12p @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V13q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) )
| ( ( V12p @ V0t0 )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V14q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V13q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V14q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ( (~) @ ( V12p @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V13q1_2E0 ) ) ) ) ) ) )
| ( ( V12p @ V0t0 )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V14q2_2E0 ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__G,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ! [V3t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
<=> ? [V4t: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( ( ! [V5t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
& ! [V6t: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
<=> ! [V7t: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
& ( ( ! [V8t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
| ! [V9t: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ? [V10p: mono_2Etyop_2Enum_2Enum > $o,V11q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V10p @ V0t0 ) )
& ( (~) @ ( V11q @ V0t0 ) )
& ! [V12t: mono_2Etyop_2Enum_2Enum] :
( ( ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) )
& ( ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) ) )
& ! [V13t: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
| ( (~) @ ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__F,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ? [V3t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
<=> ! [V4t: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( ( ? [V5t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
| ? [V6t: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
<=> ? [V7t: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
& ( ( ? [V8t: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
& ? [V9t: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ? [V10p: mono_2Etyop_2Enum_2Enum > $o,V11q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V10p @ V0t0 ) )
& ( (~) @ ( V11q @ V0t0 ) )
& ! [V12t: mono_2Etyop_2Enum_2Enum] :
( ( ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) )
& ( ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) )
& ? [V13t: mono_2Etyop_2Enum_2Enum] :
( ( V10p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__FG,axiom,
! [F0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V2a: mono_2Etyop_2Enum_2Enum > $o,V18t: mono_2Etyop_2Enum_2Enum,V0t0: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V2a @ V18t @ V0t0 )
<=> ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ? [V3t1: mono_2Etyop_2Enum_2Enum] :
! [V4t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V3t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t2 @ V0t0 ) ) ) )
<=> ! [V5t1: mono_2Etyop_2Enum_2Enum] :
? [V6t2: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ( ? [V7t1: mono_2Etyop_2Enum_2Enum] :
! [V8t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
& ? [V9t1: mono_2Etyop_2Enum_2Enum] :
! [V10t2: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) )
<=> ? [V11t1: mono_2Etyop_2Enum_2Enum] :
! [V12t2: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) )
& ( ( ? [V13t1: mono_2Etyop_2Enum_2Enum] :
! [V14t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t2 @ V0t0 ) ) )
| ? [V15t1: mono_2Etyop_2Enum_2Enum] :
! [V16t2: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
<=> ? [V17q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V17q @ V0t0 ) )
& ! [V18t: mono_2Etyop_2Enum_2Enum] :
( ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( F0 @ V2a @ V18t @ V0t0 ) ) )
& ? [V19t1: mono_2Etyop_2Enum_2Enum] :
! [V20t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__GF,axiom,
! [F0: ( mono_2Etyop_2Enum_2Enum > $o ) > mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1b: mono_2Etyop_2Enum_2Enum > $o,V18t: mono_2Etyop_2Enum_2Enum,V0t0: mono_2Etyop_2Enum_2Enum] :
( ( F0 @ V1b @ V18t @ V0t0 )
<=> ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ! [V3t1: mono_2Etyop_2Enum_2Enum] :
? [V4t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V3t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t2 @ V0t0 ) ) ) )
<=> ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ( ! [V7t1: mono_2Etyop_2Enum_2Enum] :
? [V8t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
| ! [V9t1: mono_2Etyop_2Enum_2Enum] :
? [V10t2: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) )
<=> ! [V11t1: mono_2Etyop_2Enum_2Enum] :
? [V12t2: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) )
& ( ( ! [V13t1: mono_2Etyop_2Enum_2Enum] :
? [V14t2: mono_2Etyop_2Enum_2Enum] : ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t2 @ V0t0 ) ) )
& ! [V15t1: mono_2Etyop_2Enum_2Enum] :
? [V16t2: mono_2Etyop_2Enum_2Enum] : ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
<=> ? [V17q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V17q @ V0t0 ) )
& ! [V18t: mono_2Etyop_2Enum_2Enum] :
( ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( F0 @ V1b @ V18t @ V0t0 ) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) )
& ! [V19t1: mono_2Etyop_2Enum_2Enum] :
? [V20t2: mono_2Etyop_2Enum_2Enum] :
( ( V17q @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__G,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ! [V2t: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V2t @ V0t0 ) )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V3q @ V0t0 )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ? [V5t: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) )
& ( ! [V6t: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) )
<=> ? [V7q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V7q @ V0t0 )
& ! [V8t: mono_2Etyop_2Enum_2Enum] :
( ( V7q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
<=> ( ( V7q @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
& ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) )
& ? [V9t1: mono_2Etyop_2Enum_2Enum] :
! [V10t2: mono_2Etyop_2Enum_2Enum] : ( V7q @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) ) )
& ( ! [V11t: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
<=> ? [V12q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V12q @ V0t0 )
& ! [V13t: mono_2Etyop_2Enum_2Enum] :
( ( V12q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
<=> ( ( V12q @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) )
& ! [V14t1: mono_2Etyop_2Enum_2Enum] :
? [V15t2: mono_2Etyop_2Enum_2Enum] : ( V12q @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__F,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ? [V2t: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V2t @ V0t0 ) )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( V3q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
<=> ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ? [V7t: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
<=> ? [V8q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V8q @ V0t0 ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] :
( ( V8q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ( ( V8q @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) )
| ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) )
& ! [V10t1: mono_2Etyop_2Enum_2Enum] :
? [V11t2: mono_2Etyop_2Enum_2Enum] : ( V8q @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__FG,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ? [V2t1: mono_2Etyop_2Enum_2Enum] :
! [V3t2: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V2t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V3t2 @ V0t0 ) ) )
<=> ? [V4q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V4q @ V0t0 ) )
& ! [V5t: mono_2Etyop_2Enum_2Enum] :
( ( V4q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
=> ( ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
& ( V4q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) )
& ? [V6t: mono_2Etyop_2Enum_2Enum] : ( V4q @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) )
& ( ? [V7t1: mono_2Etyop_2Enum_2Enum] :
! [V8t2: mono_2Etyop_2Enum_2Enum] : ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V7t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
<=> ? [V9p: mono_2Etyop_2Enum_2Enum > $o,V10q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V9p @ V0t0 ) )
& ( (~) @ ( V10q @ V0t0 ) )
& ! [V11t: mono_2Etyop_2Enum_2Enum] :
( ( ( V9p @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
=> ( V9p @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
& ( ( V9p @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
=> ( ( V9p @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
| ( (~) @ ( V10q @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) )
& ( ( V10q @ ( mono_2Ec_2Enum_2ESUC @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
<=> ( ( ( V9p @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
& ( (~) @ ( V10q @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
& ( (~) @ ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
| ( ( V9p @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
& ( V10q @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) )
& ! [V12t1: mono_2Etyop_2Enum_2Enum] :
? [V13t2: mono_2Etyop_2Enum_2Enum] :
( ( V9p @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t2 @ V0t0 ) ) )
& ( (~) @ ( V10q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ETEMP__OPS__DEFS__TO__OMEGA,axiom,
! [V0l: mono_2Etyop_2Enum_2Enum > $o,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2ENEXT @ V2a ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V3t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V3t )
= ( V2a @ ( mono_2Ec_2Enum_2ESUC @ V3t ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2EALWAYS @ V2a ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V4t )
<=> ( ( V2a @ V4t )
& ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V4t ) ) ) )
& ! [V5t1: mono_2Etyop_2Enum_2Enum] :
? [V6t2: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ V6t2 ) )
=> ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ V6t2 ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V7t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V7t )
<=> ( ( V2a @ V7t )
| ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V7t ) ) ) )
& ! [V8t1: mono_2Etyop_2Enum_2Enum] :
? [V9t2: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t1 @ V9t2 ) )
=> ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t1 @ V9t2 ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V10t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V10t )
<=> ( ( (~) @ ( V1b @ V10t ) )
=> ( ( V2a @ V10t )
& ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V10t ) ) ) ) )
& ! [V11t1: mono_2Etyop_2Enum_2Enum] :
? [V12t2: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) )
=> ( ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V13t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V13t )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V1b @ V13t ) @ ( V2a @ V13t ) @ ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V13t ) ) ) )
& ! [V14t1: mono_2Etyop_2Enum_2Enum] :
? [V15t2: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ V15t2 ) )
=> ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ V15t2 ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V16t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V16t )
<=> ( ( (~) @ ( V1b @ V16t ) )
& ( ( V2a @ V16t )
| ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V16t ) ) ) ) )
& ! [V17t1: mono_2Etyop_2Enum_2Enum] :
? [V18t2: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
=> ( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V19t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V19t )
<=> ( ( (~) @ ( V1b @ V19t ) )
=> ( ( V2a @ V19t )
& ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V19t ) ) ) ) )
& ! [V20t1: mono_2Etyop_2Enum_2Enum] :
? [V21t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) )
=> ( ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V22t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V22t )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V1b @ V22t ) @ ( V2a @ V22t ) @ ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V22t ) ) ) )
& ! [V23t1: mono_2Etyop_2Enum_2Enum] :
? [V24t2: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V23t1 @ V24t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V23t1 @ V24t2 ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
<=> ( mono_2Ec_2Ebool_2ET
& ! [V25t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ V25t )
<=> ( ( (~) @ ( V1b @ V25t ) )
& ( ( V2a @ V25t )
| ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V25t ) ) ) ) )
& ! [V26t1: mono_2Etyop_2Enum_2Enum] :
? [V27t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V0l @ ( mono_2Ec_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) ) )
=> ( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) ) ) ) ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ V2a ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V28t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V28t ) )
= ( V2a @ V28t ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ V2a ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V29t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V29t ) )
= ( V2a @ V29t ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V30t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V30t ) )
<=> ( ( V2a @ V30t )
& ( V0l @ V30t ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V31t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V31t ) )
<=> ( ( V2a @ V31t )
| ( V0l @ V31t ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V32t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V32t ) )
<=> ( ( V1b @ V32t )
| ( ( V2a @ V32t )
& ( V0l @ V32t ) ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V33t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V33t ) )
<=> ( ( ( V2a @ V33t )
& ( V1b @ V33t ) )
| ( ( (~) @ ( V1b @ V33t ) )
& ( V0l @ V33t ) ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2EF )
& ! [V34t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V34t ) )
<=> ( ( (~) @ ( V1b @ V34t ) )
& ( ( V2a @ V34t )
| ( V0l @ V34t ) ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V35t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V35t ) )
<=> ( ( V1b @ V35t )
| ( ( V2a @ V35t )
& ( V0l @ V35t ) ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V36t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V36t ) )
<=> ( ( ( V2a @ V36t )
& ( V1b @ V36t ) )
| ( ( (~) @ ( V1b @ V36t ) )
& ( V0l @ V36t ) ) ) )
& mono_2Ec_2Ebool_2ET ) )
& ( ( V0l
= ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ mono_2Ec_2Enum_2E0 )
= mono_2Ec_2Ebool_2ET )
& ! [V37t: mono_2Etyop_2Enum_2Enum] :
( ( V0l @ ( mono_2Ec_2Enum_2ESUC @ V37t ) )
<=> ( ( (~) @ ( V1b @ V37t ) )
& ( ( V2a @ V37t )
| ( V0l @ V37t ) ) ) )
& mono_2Ec_2Ebool_2ET ) ) ) ).
thf(thm_2EOmega__Automata_2EAUTOMATON__TEMP__CLOSURE,axiom,
! [A_27a: d,A_27b: d,V0phi: mono_2Etyop_2Enum_2Enum > $o,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o,V3Phi__R2_2E0: u,V4Phi__R1_2E0: u,V5Phi__I2_2E0: u,V6Phi__I1_2E0: u,V7Phi__F_2E0: u,V8Phi: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( ? [V9q1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V6Phi__I1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V9q1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V4Phi__R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V9q1_2E0 ) ) ) )
& ? [V10q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__I2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V10q2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V3Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V10q2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V9q1_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V7Phi__F_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V9q1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V10q2_2E0 ) ) ) ) ) ) ) )
<=> ? [V11q1_2E0: u,V12q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V6Phi__I1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V11q1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__I2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q2_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ tyop_2Emin_2Ebool ) @ V4Phi__R1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V11q1_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ tyop_2Emin_2Ebool ) @ V3Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q2_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V11q1_2E0 ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ tyop_2Emin_2Ebool ) @ V7Phi__F_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V11q1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q2_2E0 ) ) ) ) ) ) ) )
& ( ( V8Phi @ ( mono_2Ec_2ETemporal__Logic_2ENEXT @ V0phi ) )
<=> ? [V13q0: mono_2Etyop_2Enum_2Enum > $o,V14q1: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( V13q0 @ V15t )
= ( V0phi @ V15t ) )
& ( ( V14q1 @ V15t )
= ( V13q0 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V8Phi @ V14q1 ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ V0phi ) )
<=> ? [V16q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V16q @ mono_2Ec_2Enum_2E0 )
& ! [V17t: mono_2Etyop_2Enum_2Enum] :
( ( V16q @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= ( V0phi @ V17t ) )
& ( V8Phi @ V16q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ V0phi ) )
<=> ? [V18q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V18q @ mono_2Ec_2Enum_2E0 ) )
& ! [V19t: mono_2Etyop_2Enum_2Enum] :
( ( V18q @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
= ( V0phi @ V19t ) )
& ( V8Phi @ V18q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
<=> ? [V20q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V20q @ mono_2Ec_2Enum_2E0 )
& ! [V21t: mono_2Etyop_2Enum_2Enum] :
( ( V20q @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V2a @ V21t )
& ( V20q @ V21t ) ) )
& ( V8Phi @ V20q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
<=> ? [V22q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V22q @ mono_2Ec_2Enum_2E0 ) )
& ! [V23t: mono_2Etyop_2Enum_2Enum] :
( ( V22q @ ( mono_2Ec_2Earithmetic_2E_2B @ V23t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V2a @ V23t )
| ( V22q @ V23t ) ) )
& ( V8Phi @ V22q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
<=> ? [V24q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V24q @ mono_2Ec_2Enum_2E0 ) )
& ! [V25t: mono_2Etyop_2Enum_2Enum] :
( ( V24q @ ( mono_2Ec_2Earithmetic_2E_2B @ V25t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V1b @ V25t )
| ( ( V2a @ V25t )
& ( V24q @ V25t ) ) ) )
& ( V8Phi @ V24q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
<=> ? [V26q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V26q @ mono_2Ec_2Enum_2E0 ) )
& ! [V27t: mono_2Etyop_2Enum_2Enum] :
( ( V26q @ ( mono_2Ec_2Earithmetic_2E_2B @ V27t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( ( V2a @ V27t )
& ( V1b @ V27t ) )
| ( ( (~) @ ( V1b @ V27t ) )
& ( V26q @ V27t ) ) ) )
& ( V8Phi @ V26q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
<=> ? [V28q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V28q @ mono_2Ec_2Enum_2E0 ) )
& ! [V29t: mono_2Etyop_2Enum_2Enum] :
( ( V28q @ ( mono_2Ec_2Earithmetic_2E_2B @ V29t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( (~) @ ( V1b @ V29t ) )
& ( ( V2a @ V29t )
| ( V28q @ V29t ) ) ) )
& ( V8Phi @ V28q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
<=> ? [V30q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V30q @ mono_2Ec_2Enum_2E0 )
& ! [V31t: mono_2Etyop_2Enum_2Enum] :
( ( V30q @ ( mono_2Ec_2Earithmetic_2E_2B @ V31t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V1b @ V31t )
| ( ( V2a @ V31t )
& ( V30q @ V31t ) ) ) )
& ( V8Phi @ V30q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
<=> ? [V32q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V32q @ mono_2Ec_2Enum_2E0 )
& ! [V33t: mono_2Etyop_2Enum_2Enum] :
( ( V32q @ ( mono_2Ec_2Earithmetic_2E_2B @ V33t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( ( V2a @ V33t )
& ( V1b @ V33t ) )
| ( ( (~) @ ( V1b @ V33t ) )
& ( V32q @ V33t ) ) ) )
& ( V8Phi @ V32q ) ) )
& ( ( V8Phi @ ( mono_2Ec_2EPast__Temporal__Logic_2EPNEXT @ ( mono_2Ec_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) )
<=> ? [V34q: mono_2Etyop_2Enum_2Enum > $o] :
( ( V34q @ mono_2Ec_2Enum_2E0 )
& ! [V35t: mono_2Etyop_2Enum_2Enum] :
( ( V34q @ ( mono_2Ec_2Earithmetic_2E_2B @ V35t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) )
<=> ( ( (~) @ ( V1b @ V35t ) )
& ( ( V2a @ V35t )
| ( V34q @ V35t ) ) ) )
& ( V8Phi @ V34q ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__TRANSLATION,axiom,
! [V0phi: mono_2Etyop_2Enum_2Enum > $o,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o,V3Phi: ( mono_2Etyop_2Enum_2Enum > $o ) > $o] :
( ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2ENEXT @ V0phi ) )
<=> ? [V4q0: mono_2Etyop_2Enum_2Enum > $o,V5q1: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V6t: mono_2Etyop_2Enum_2Enum] :
( ( ( V4q0 @ V6t )
= ( V0phi @ V6t ) )
& ( ( V5q1 @ V6t )
= ( V4q0 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V3Phi @ V5q1 ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2EALWAYS @ V2a ) )
<=> ? [V7q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V8t: mono_2Etyop_2Enum_2Enum] :
( ( V7q @ V8t )
<=> ( ( V2a @ V8t )
& ( V7q @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V9t1: mono_2Etyop_2Enum_2Enum] :
? [V10t2: mono_2Etyop_2Enum_2Enum] :
( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) )
=> ( V7q @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) )
& ( V3Phi @ V7q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
<=> ? [V11q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V12t: mono_2Etyop_2Enum_2Enum] :
( ( V11q @ V12t )
<=> ( ( V2a @ V12t )
| ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V13t1: mono_2Etyop_2Enum_2Enum] :
? [V14t2: mono_2Etyop_2Enum_2Enum] :
( ( V11q @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t1 @ V14t2 ) )
=> ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t1 @ V14t2 ) ) )
& ( V3Phi @ V11q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) )
<=> ? [V15q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V16t: mono_2Etyop_2Enum_2Enum] :
( ( V15q @ V16t )
<=> ( ( V1b @ V16t )
| ( ( V2a @ V16t )
& ( V15q @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V17t1: mono_2Etyop_2Enum_2Enum] :
? [V18t2: mono_2Etyop_2Enum_2Enum] :
( ( V15q @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
=> ( ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) ) )
& ( V3Phi @ V15q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
<=> ? [V19q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V20t: mono_2Etyop_2Enum_2Enum] :
( ( V19q @ V20t )
<=> ( ( V1b @ V20t )
| ( ( V2a @ V20t )
& ( V19q @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V21t1: mono_2Etyop_2Enum_2Enum] :
? [V22t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V19q @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) )
=> ( ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) ) )
& ( V3Phi @ V19q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) )
<=> ? [V23q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V24t: mono_2Etyop_2Enum_2Enum] :
( ( V23q @ V24t )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V1b @ V24t ) @ ( V2a @ V24t ) @ ( V23q @ ( mono_2Ec_2Earithmetic_2E_2B @ V24t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V25t1: mono_2Etyop_2Enum_2Enum] :
? [V26t2: mono_2Etyop_2Enum_2Enum] :
( ( V23q @ ( mono_2Ec_2Earithmetic_2E_2B @ V25t1 @ V26t2 ) )
=> ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V25t1 @ V26t2 ) ) )
& ( V3Phi @ V23q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
<=> ? [V27q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V28t: mono_2Etyop_2Enum_2Enum] :
( ( V27q @ V28t )
= ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V1b @ V28t ) @ ( V2a @ V28t ) @ ( V27q @ ( mono_2Ec_2Earithmetic_2E_2B @ V28t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V29t1: mono_2Etyop_2Enum_2Enum] :
? [V30t2: mono_2Etyop_2Enum_2Enum] :
( ( V27q @ ( mono_2Ec_2Earithmetic_2E_2B @ V29t1 @ V30t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V29t1 @ V30t2 ) ) )
& ( V3Phi @ V27q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) )
<=> ? [V31q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V32t: mono_2Etyop_2Enum_2Enum] :
( ( V31q @ V32t )
<=> ( ( (~) @ ( V1b @ V32t ) )
& ( ( V2a @ V32t )
| ( V31q @ ( mono_2Ec_2Earithmetic_2E_2B @ V32t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V33t1: mono_2Etyop_2Enum_2Enum] :
? [V34t2: mono_2Etyop_2Enum_2Enum] :
( ( V31q @ ( mono_2Ec_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) )
=> ( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) ) ) )
& ( V3Phi @ V31q ) ) )
& ( ( V3Phi @ ( mono_2Ec_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
<=> ? [V35q: mono_2Etyop_2Enum_2Enum > $o] :
( mono_2Ec_2Ebool_2ET
& ! [V36t: mono_2Etyop_2Enum_2Enum] :
( ( V35q @ V36t )
<=> ( ( (~) @ ( V1b @ V36t ) )
& ( ( V2a @ V36t )
| ( V35q @ ( mono_2Ec_2Earithmetic_2E_2B @ V36t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V37t1: mono_2Etyop_2Enum_2Enum] :
? [V38t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V35q @ ( mono_2Ec_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) ) )
=> ( ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) )
| ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) ) ) )
& ( V3Phi @ V35q ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__CONJ__CLOSURE,axiom,
! [A_27a: d,A_27b1: d,A_27b2: d,V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2Psi2_2E0: u,V3Psi1_2E0: u,V4Phi__R2_2E0: u,V5Phi__R1_2E0: u,V6Phi__I2_2E0: u,V7Phi__I1_2E0: u] :
( ( ? [V8q1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V8q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) )
& ? [V12q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V12q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V13t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V12q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ? [V14t1: mono_2Etyop_2Enum_2Enum] :
! [V15t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V12q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ? [V16q1_2E0: u,V17q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V7Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V16q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V6Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V17q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V18t: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V16q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V4Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V17q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) ) ) ) ) ) ) )
& ? [V19t1: mono_2Etyop_2Enum_2Enum] :
! [V20t2: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V3Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V16q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V2Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V17q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V19t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__DISJ__CLOSURE,axiom,
! [A_27a: d,A_27b1: d,A_27b2: d,V0t0: mono_2Etyop_2Enum_2Enum,V1t: mono_2Etyop_2Enum_2Enum,V2i_2E0: u,V3Psi2_2E0: u,V4Psi1_2E0: u,V5Phi__R2_2E0: u,V6Phi__R1_2E0: u,V7Phi__I2_2E0: u,V8Phi__I1_2E0: u] :
( ( ? [V9q1_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V8Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V9q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V10t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V6Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V9q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ? [V11t1: mono_2Etyop_2Enum_2Enum] :
! [V12t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V4Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V9q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) )
| ? [V13q2_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V7Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) )
& ! [V14t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ? [V15t1: mono_2Etyop_2Enum_2Enum] :
! [V16t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V3Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V13q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) )
<=> ? [V17p: mono_2Etyop_2Enum_2Enum > $o,V18q1_2E0: u,V19q2_2E0: u] :
( ( ( ( (~) @ ( V17p @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b1 @ tyop_2Emin_2Ebool ) @ V8Phi__I1_2E0 ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V18q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) )
| ( ( V17p @ V0t0 )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b2 @ tyop_2Emin_2Ebool ) @ V7Phi__I2_2E0 ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V19q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V20t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V6Phi__R1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V18q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( (~) @ ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V5Phi__R2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V19q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V20t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V21t1: mono_2Etyop_2Enum_2Enum] :
! [V22t2: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V1t @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ tyop_2Emin_2Ebool ) @ V4Psi1_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b1 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b1 ) @ V18q1_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V17p @ ( mono_2Ec_2Earithmetic_2E_2B @ V1t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ tyop_2Emin_2Ebool ) @ V3Psi2_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b2 @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b2 ) @ V19q2_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V21t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__NEXT__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V5Phi__I_2E0: u,V4Phi__R_2E0: u,V1i_2E0: u,V3Psi_2E0: u,V6t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3Psi_2E0 ) ) ) @ V6t0 )
<=> ? [V7q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V6t0 ) ) ) ) ) ) )
& ! [V8t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V6t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ V6t0 ) ) ) ) ) ) ) ) ) )
& ? [V9t1: mono_2Etyop_2Enum_2Enum] :
! [V10t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t2 @ V6t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t2 @ V6t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1i_2E0: u,V2c_2E0: u,V3Psi_2E0: u,V4Phi__R_2E0: u,V5Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2ENEXT @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3Psi_2E0 ) ) ) ) @ V0t0 )
<=> ? [V11p: mono_2Etyop_2Enum_2Enum > $o,V12q_2E0: u] :
( ( ( V11p @ V0t0 )
= mono_2Ec_2Ebool_2EF )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V2c_2E0 ) )
& ! [V13t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V11p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V2c_2E0 ) )
& ( V11p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V5Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V11p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V11p @ ( mono_2Ec_2Earithmetic_2E_2B @ V13t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V14t1: mono_2Etyop_2Enum_2Enum] :
! [V15t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V3Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V1i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V12q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SUNTIL__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V13q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V3c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ A_27b @ V3c_2E0 ) ) ) )
<=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
=> ( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2ESUNTIL @ V1phi @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V0t0 )
<=> ? [V12p: mono_2Etyop_2Enum_2Enum > $o,V13q_2E0: u] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V12p @ V0t0 ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ A_27b @ V3c_2E0 ) ) ) ) )
& ! [V14t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V15t1: mono_2Etyop_2Enum_2Enum] :
! [V16t2: mono_2Etyop_2Enum_2Enum] :
( ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__UNTIL__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F1_2E0: u,F0_2E0: u] :
( ! [V13q_2E0: u,V0t0: mono_2Etyop_2Enum_2Enum,V3c_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ A_27b @ V3c_2E0 ) ) ) )
<=> ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
=> ( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2EUNTIL @ V1phi @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V0t0 )
<=> ? [V12p: mono_2Etyop_2Enum_2Enum > $o,V13q_2E0: u] :
( ( mono_2Ec_2Ebool_2ECOND_2Emono_2Etyop_2Emin_2Ebool @ ( V12p @ V0t0 ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) @ ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) ) ) @ F1_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) ) ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) @ ( s @ A_27b @ V3c_2E0 ) ) ) ) )
& ! [V14t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V14t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V15t1: mono_2Etyop_2Enum_2Enum] :
! [V16t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V12p @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V13q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SBEFORE__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2ESBEFORE @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V1phi @ V0t0 )
<=> ? [V12p1: mono_2Etyop_2Enum_2Enum > $o,V13p2: mono_2Etyop_2Enum_2Enum > $o,V14q_2E0: u] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: mono_2Etyop_2Enum_2Enum] :
! [V17t2: mono_2Etyop_2Enum_2Enum] :
( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__BEFORE__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2EBEFORE @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V1phi @ V0t0 )
<=> ? [V12p1: mono_2Etyop_2Enum_2Enum > $o,V13p2: mono_2Etyop_2Enum_2Enum > $o,V14q_2E0: u] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: mono_2Etyop_2Enum_2Enum] :
! [V17t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SWHEN__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2ESWHEN @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V1phi @ V0t0 )
<=> ? [V12p1: mono_2Etyop_2Enum_2Enum > $o,V13p2: mono_2Etyop_2Enum_2Enum > $o,V14q_2E0: u] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: mono_2Etyop_2Enum_2Enum] :
! [V17t2: mono_2Etyop_2Enum_2Enum] :
( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__WHEN__CLOSURE,axiom,
! [A_27a: d,A_27b: d,F0_2E0: u] :
( ! [V6Phi__I_2E0: u,V5Phi__R_2E0: u,V2i_2E0: u,V4Psi_2E0: u,V7t0: mono_2Etyop_2Enum_2Enum] :
( ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) @ V7t0 )
<=> ? [V8q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V7t0 ) ) ) ) ) ) )
& ! [V9t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) ) ) ) ) ) )
& ? [V10t1: mono_2Etyop_2Enum_2Enum] :
! [V11t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V8q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V10t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [V0t0: mono_2Etyop_2Enum_2Enum,V1phi: mono_2Etyop_2Enum_2Enum > $o,V2i_2E0: u,V3c_2E0: u,V4Psi_2E0: u,V5Phi__R_2E0: u,V6Phi__I_2E0: u] :
( ( mono_2Ec_2ETemporal__Logic_2EWHEN @ ( j_mono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ tyop_2Emin_2Ebool ) ) ) ) ) @ F0_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) ) ) @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) ) ) ) @ V1phi @ V0t0 )
<=> ? [V12p1: mono_2Etyop_2Enum_2Enum > $o,V13p2: mono_2Etyop_2Enum_2Enum > $o,V14q_2E0: u] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V0t0 ) ) ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) ) )
| ( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) )
= ( s @ A_27b @ V3c_2E0 ) )
& ( (~) @ ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V1phi @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27b @ tyop_2Emin_2Ebool ) @ V6Phi__I_2E0 ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V5Phi__R_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) ) ) ) ) ) ) )
& ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V0t0 @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: mono_2Etyop_2Enum_2Enum] :
! [V17t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V12p1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) )
| ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ tyop_2Emin_2Ebool ) @ V4Psi_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V2i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) @ ( s @ A_27b @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27b ) @ V14q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V16t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ENEXT__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2ENEXT @ V1a @ V0t0 )
<=> ? [V2p: mono_2Etyop_2Enum_2Enum > $o,V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V2p @ V0t0 ) )
& ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V2p @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESUNTIL__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EUNTIL__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESBEFORE__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBEFORE__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESWHEN__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] : ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EWHEN__AS__CO__BUECHI,axiom,
! [V0t0: mono_2Etyop_2Enum_2Enum,V1b: mono_2Etyop_2Enum_2Enum > $o,V2a: mono_2Etyop_2Enum_2Enum > $o] :
( ( mono_2Ec_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3q: mono_2Etyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: mono_2Etyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1b @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V4t @ ( mono_2Ec_2Earithmetic_2E_2B @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: mono_2Etyop_2Enum_2Enum] :
! [V6t2: mono_2Etyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( mono_2Ec_2Earithmetic_2E_2B @ V5t1 @ ( mono_2Ec_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PERIODIC__MODEL,axiom,
! [A_27a: d,A_27state: d,V0TransRel_2E0: u,V1InitState_2E0: u,V2Accept_2E0: u] :
( ! [V3s_2E0: u] :
? [V4x0: mono_2Etyop_2Enum_2Enum,V5l: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V5l )
& ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x0 ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) ) ) ) )
=> ( ? [V6i_2E0: u,V7q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V8t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V6i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V9t1: mono_2Etyop_2Enum_2Enum] :
? [V10t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) ) ) ) ) ) )
<=> ? [V11x0: mono_2Etyop_2Enum_2Enum,V12l: mono_2Etyop_2Enum_2Enum,V13j_2E0: u,V14p_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V12l )
& ! [V15t2: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V15t2 ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ ( mono_2Ec_2Earithmetic_2EMOD @ V15t2 @ V12l ) ) ) ) ) ) )
& ! [V16t2: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V16t2 ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ ( mono_2Ec_2Earithmetic_2EMOD @ V16t2 @ V12l ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V17t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V18t1: mono_2Etyop_2Enum_2Enum] :
? [V19t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V18t1 @ V19t2 ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PERIODIC__REDUCTION__THM,axiom,
! [A_27a: d,A_27state: d,V0TransRel_2E0: u,V1InitState_2E0: u,V2Accept_2E0: u] :
( ! [V3s_2E0: u] :
? [V4x0: mono_2Etyop_2Enum_2Enum,V5l: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V5l )
& ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x0 ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) ) ) ) )
=> ( ? [V6i_2E0: u,V7q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V8t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V6i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V9t1: mono_2Etyop_2Enum_2Enum] :
? [V10t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) ) ) ) ) ) )
<=> ? [V11x0: mono_2Etyop_2Enum_2Enum,V12l: mono_2Etyop_2Enum_2Enum,V13j_2E0: u,V14p_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V12l )
& ! [V15t2: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V15t2 ) ) ) ) )
= ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ ( mono_2Ec_2Earithmetic_2EMOD @ V15t2 @ V12l ) ) ) ) ) ) )
& ! [V16t2: mono_2Etyop_2Enum_2Enum] :
( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V16t2 ) ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ ( mono_2Ec_2Earithmetic_2EMOD @ V16t2 @ V12l ) ) ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V17t: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V17t @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V12l ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V17t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V17t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ? [V18t: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V18t @ V12l )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V18t ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PROP__REDUCTION,axiom,
! [A_27a: d,A_27state: d,V0TransRel_2E0: u,V1InitState_2E0: u,V2Accept_2E0: u] :
( ! [V3s_2E0: u] :
? [V4x0: mono_2Etyop_2Enum_2Enum,V5l: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V5l )
& ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V4x0 ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V3s_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) ) ) ) )
=> ( ? [V6i_2E0: u,V7q_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V8t: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V6i_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V8t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V8t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ! [V9t1: mono_2Etyop_2Enum_2Enum] :
? [V10t2: mono_2Etyop_2Enum_2Enum] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V7q_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) ) ) ) ) ) )
<=> ? [V11x0: mono_2Etyop_2Enum_2Enum,V12l: mono_2Etyop_2Enum_2Enum,V13j_2E0: u,V14p_2E0: u] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ mono_2Ec_2Enum_2E0 @ V12l )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V1InitState_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ mono_2Ec_2Enum_2E0 ) ) ) ) ) ) )
& ! [V15t: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V15t @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V12l ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ tyop_2Emin_2Ebool ) @ V0TransRel_2E0 ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27a @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27a ) @ V13j_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15t ) ) ) ) @ ( s @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( c_2Epair_2E_2C_2E2 @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V15t ) ) ) ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V15t @ ( mono_2Ec_2Earithmetic_2ENUMERAL @ ( mono_2Ec_2Earithmetic_2EBIT1 @ mono_2Ec_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
& ? [V16t: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V16t @ V12l )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27state @ tyop_2Emin_2Ebool ) @ V2Accept_2E0 ) @ ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V16t ) ) ) ) ) ) ) ) )
& ( ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ V11x0 ) ) ) )
= ( s @ A_27state @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ tyop_2Enum_2Enum @ A_27state ) @ V14p_2E0 ) @ ( s @ tyop_2Enum_2Enum @ ( i_mono_2Etyop_2Enum_2Enum @ ( mono_2Ec_2Earithmetic_2E_2B @ V11x0 @ V12l ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EEQUALITY__THM,axiom,
! [A_27a: d,V0x_2E0: u,V1y_2E0: u] :
( ( ( s @ A_27a @ V0x_2E0 )
= ( s @ A_27a @ V1y_2E0 ) )
<=> ! [V2P_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V0x_2E0 ) ) ) )
= ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2P_2E0 ) @ ( s @ A_27a @ V1y_2E0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ELESS__THM,axiom,
! [V0x: mono_2Etyop_2Enum_2Enum,V1y: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V0x @ V1y )
<=> ? [V2P: mono_2Etyop_2Enum_2Enum > $o] :
( ( V2P @ V0x )
& ( (~) @ ( V2P @ V1y ) )
& ! [V3z: mono_2Etyop_2Enum_2Enum] :
( ( V2P @ ( mono_2Ec_2Enum_2ESUC @ V3z ) )
=> ( V2P @ V3z ) ) ) ) ).
thf(thm_2EOmega__Automata_2EFORALL__EXISTS__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ! [V1t1: mono_2Etyop_2Enum_2Enum] :
? [V2t2: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Earithmetic_2E_2B @ V1t1 @ V2t2 ) )
<=> ! [V3t1: mono_2Etyop_2Enum_2Enum] :
? [V4t2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3t1 @ V4t2 )
& ( V0P @ V4t2 ) ) ) ).
thf(thm_2EOmega__Automata_2EEXISTS__FORALL__THM,axiom,
! [V0P: mono_2Etyop_2Enum_2Enum > $o] :
( ? [V1t1: mono_2Etyop_2Enum_2Enum] :
! [V2t2: mono_2Etyop_2Enum_2Enum] : ( V0P @ ( mono_2Ec_2Earithmetic_2E_2B @ V1t1 @ V2t2 ) )
<=> ? [V3t1: mono_2Etyop_2Enum_2Enum] :
! [V4t2: mono_2Etyop_2Enum_2Enum] :
( ( mono_2Ec_2Eprim__rec_2E_3C @ V3t1 @ V4t2 )
=> ( V0P @ V4t2 ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT__LEMMA,axiom,
! [A_27a: d,V0PHI_2E0: u] :
( ? [V1x_2E0: u] :
! [V2p_2E0: u] : ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2p_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
<=> ? [V3q_2E0: u] :
( ! [V4x_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V4x_2E0 ) ) ) )
=> ! [V5p_2E0: u] : ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V5p_2E0 ) ) ) @ ( s @ A_27a @ V4x_2E0 ) ) ) ) )
& ? [V6z_2E0: u] : ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V6z_2E0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT1__THM,axiom,
! [A_27a: d,V0PHI_2E0: u] :
( ? [V1x_2E0: u] :
! [V2p_2E0: u] : ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2p_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
<=> ? [V3q_2E0: u] :
! [V4p_2E0: u,V5x_2E0: u] :
? [V6z_2E0: u] :
( ( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
=> ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4p_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V6z_2E0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT2__THM,axiom,
! [A_27a: d,V0PHI_2E0: u] :
( ! [V1x_2E0: u] :
? [V2p_2E0: u] : ( 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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V2p_2E0 ) ) ) @ ( s @ A_27a @ V1x_2E0 ) ) ) )
<=> ! [V3q_2E0: u] :
? [V4p_2E0: u,V5x_2E0: u] :
! [V6z_2E0: u] :
( ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V6z_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 @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) ) @ V0PHI_2E0 ) @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V4p_2E0 ) ) ) @ ( s @ A_27a @ V5x_2E0 ) ) ) )
& ( j_mono_2Etyop_2Emin_2Ebool @ ( s @ tyop_2Emin_2Ebool @ ( app_2E2 @ ( s @ ( tyop_2Emin_2Efun @ A_27a @ tyop_2Emin_2Ebool ) @ V3q_2E0 ) @ ( s @ A_27a @ V5x_2E0 ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------