ITP001 Axioms: ITP080^7.ax
%------------------------------------------------------------------------------
% File : ITP080^7 : 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]
% : HL4080^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 89 ( 7 unt; 42 typ; 0 def)
% Number of atoms : 438 ( 88 equ; 174 cnn)
% Maximal formula atoms : 66 ( 4 avg)
% Number of connectives : 4568 ( 174 ~; 98 |; 516 &;3616 @)
% ( 133 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 19 avg;3616 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 423 ( 423 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 40 usr; 5 con; 0-4 aty)
% Number of variables : 651 ( 39 ^ 403 !; 203 ?; 651 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TH1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
thf(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: $tType > $tType > $tType ).
thf(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
thf(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: $tType > $tType > $tType ).
thf(c_2Ebool_2E_21,type,
c_2Ebool_2E_21:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2Earithmetic_2E_2B,type,
c_2Earithmetic_2E_2B: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Epair_2E_2C,type,
c_2Epair_2E_2C:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > A_27b > ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) ) ).
thf(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(c_2Enum_2E0,type,
c_2Enum_2E0: tyop_2Enum_2Enum ).
thf(c_2Eprim__rec_2E_3C,type,
c_2Eprim__rec_2E_3C: tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o ).
thf(c_2Emin_2E_3D,type,
c_2Emin_2E_3D:
!>[A_27a: $tType] : ( A_27a > A_27a > $o ) ).
thf(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F:
!>[A_27a: $tType] : ( ( A_27a > $o ) > $o ) ).
thf(c_2ETemporal__Logic_2EALWAYS,type,
c_2ETemporal__Logic_2EALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2EBEFORE,type,
c_2ETemporal__Logic_2EBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EBIT1,type,
c_2Earithmetic_2EBIT1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2Ebool_2ECOND,type,
c_2Ebool_2ECOND:
!>[A_27a: $tType] : ( $o > A_27a > A_27a > A_27a ) ).
thf(c_2ETemporal__Logic_2EEVENTUAL,type,
c_2ETemporal__Logic_2EEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2EF,type,
c_2Ebool_2EF: $o ).
thf(c_2Earithmetic_2EMOD,type,
c_2Earithmetic_2EMOD: tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2ETemporal__Logic_2ENEXT,type,
c_2ETemporal__Logic_2ENEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2ENUMERAL,type,
c_2Earithmetic_2ENUMERAL: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2EPast__Temporal__Logic_2EPALWAYS,type,
c_2EPast__Temporal__Logic_2EPALWAYS: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPBEFORE,type,
c_2EPast__Temporal__Logic_2EPBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPEVENTUAL,type,
c_2EPast__Temporal__Logic_2EPEVENTUAL: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPNEXT,type,
c_2EPast__Temporal__Logic_2EPNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSBEFORE,type,
c_2EPast__Temporal__Logic_2EPSBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSNEXT,type,
c_2EPast__Temporal__Logic_2EPSNEXT: ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSUNTIL,type,
c_2EPast__Temporal__Logic_2EPSUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPSWHEN,type,
c_2EPast__Temporal__Logic_2EPSWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPUNTIL,type,
c_2EPast__Temporal__Logic_2EPUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2EPast__Temporal__Logic_2EPWHEN,type,
c_2EPast__Temporal__Logic_2EPWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ESBEFORE,type,
c_2ETemporal__Logic_2ESBEFORE: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Enum_2ESUC,type,
c_2Enum_2ESUC: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
thf(c_2ETemporal__Logic_2ESUNTIL,type,
c_2ETemporal__Logic_2ESUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2ESWHEN,type,
c_2ETemporal__Logic_2ESWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Ebool_2ET,type,
c_2Ebool_2ET: $o ).
thf(c_2ETemporal__Logic_2EUNTIL,type,
c_2ETemporal__Logic_2EUNTIL: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2ETemporal__Logic_2EWHEN,type,
c_2ETemporal__Logic_2EWHEN: ( tyop_2Enum_2Enum > $o ) > ( tyop_2Enum_2Enum > $o ) > tyop_2Enum_2Enum > $o ).
thf(c_2Earithmetic_2EZERO,type,
c_2Earithmetic_2EZERO: tyop_2Enum_2Enum ).
thf(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $o > $o ).
thf(logicdef_2E_2F_5C,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_2F_5C @ V0 @ V1 )
<=> ( V0
& V1 ) ) ).
thf(logicdef_2E_5C_2F,axiom,
! [V0: $o,V1: $o] :
( ( c_2Ebool_2E_5C_2F @ V0 @ V1 )
<=> ( V0
| V1 ) ) ).
thf(logicdef_2E_7E,axiom,
! [V0: $o] :
( ( c_2Ebool_2E_7E @ V0 )
<=> ( (~) @ V0 ) ) ).
thf(logicdef_2E_3D_3D_3E,axiom,
! [V0: $o,V1: $o] :
( ( c_2Emin_2E_3D_3D_3E @ V0 @ V1 )
<=> ( V0
=> V1 ) ) ).
thf(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0: A_27a,V1: A_27a] :
( ( c_2Emin_2E_3D @ A_27a @ V0 @ V1 )
<=> ( V0 = V1 ) ) ).
thf(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_21 @ A_27a @ V0f )
<=> ! [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f: A_27a > $o] :
( ( c_2Ebool_2E_3F @ A_27a @ V0f )
<=> ? [V1x: A_27a] : ( V0f @ V1x ) ) ).
thf(thm_2EOmega__Automata_2EDET__OMEGA__EXISTS__FORALL__THEOREM,axiom,
! [A_27input: $tType,A_27state: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27input,V2TransRel: ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) > A_27state,V3InitVal: A_27state,V4Accept: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) ) > $o] :
( ? [V5q: tyop_2Enum_2Enum > A_27state] :
( ( ( V5q @ V0t0 )
= V3InitVal )
& ! [V6t: tyop_2Enum_2Enum] :
( ( V5q @ ( c_2Earithmetic_2E_2B @ V6t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( V2TransRel @ ( c_2Epair_2E_2C @ A_27input @ A_27state @ ( V1i @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) @ ( V5q @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) )
& ( V4Accept
@ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) @ V1i
@ ^ [V7t: tyop_2Enum_2Enum] : ( V5q @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) )
<=> ! [V8q: tyop_2Enum_2Enum > A_27state] :
( ( ( ( V8q @ V0t0 )
= V3InitVal )
& ! [V9t: tyop_2Enum_2Enum] :
( ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( V2TransRel @ ( c_2Epair_2E_2C @ A_27input @ A_27state @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) ) )
=> ( V4Accept
@ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) @ V1i
@ ^ [V10t: tyop_2Enum_2Enum] : ( V8q @ ( c_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ENEG__DET__AUTOMATA,axiom,
! [A_27input: $tType,A_27state: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27input,V2TransRel: ( tyop_2Epair_2Eprod @ A_27input @ A_27state ) > A_27state,V3InitVal: A_27state,V4Accept: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) ) > $o] :
( ( (~)
@ ? [V5q: tyop_2Enum_2Enum > A_27state] :
( ( ( V5q @ V0t0 )
= V3InitVal )
& ! [V6t: tyop_2Enum_2Enum] :
( ( V5q @ ( c_2Earithmetic_2E_2B @ V6t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( V2TransRel @ ( c_2Epair_2E_2C @ A_27input @ A_27state @ ( V1i @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) @ ( V5q @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) )
& ( V4Accept
@ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) @ V1i
@ ^ [V7t: tyop_2Enum_2Enum] : ( V5q @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) )
<=> ? [V8q: tyop_2Enum_2Enum > A_27state] :
( ( ( V8q @ V0t0 )
= V3InitVal )
& ! [V9t: tyop_2Enum_2Enum] :
( ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( V2TransRel @ ( c_2Epair_2E_2C @ A_27input @ A_27state @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) ) )
& ( (~)
@ ( V4Accept
@ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27input ) @ ( tyop_2Enum_2Enum > A_27state ) @ V1i
@ ^ [V10t: tyop_2Enum_2Enum] : ( V8q @ ( c_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EOMEGA__CONJ__CLOSURE,axiom,
! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27a,V2Psi2: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) ) > $o,V3Psi1: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) ) > $o,V4Phi__R2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V5Phi__R1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V6Phi__I2: A_27b2 > $o,V7Phi__I1: A_27b1 > $o] :
( ( ? [V8q1: tyop_2Enum_2Enum > A_27b1] :
( ( V7Phi__I1 @ ( V8q1 @ V0t0 ) )
& ! [V9t: tyop_2Enum_2Enum] : ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) @ ( V8q1 @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) )
& ( V3Psi1 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) @ V1i @ V8q1 ) ) )
& ? [V10q2: tyop_2Enum_2Enum > A_27b2] :
( ( V6Phi__I2 @ ( V10q2 @ V0t0 ) )
& ! [V11t: tyop_2Enum_2Enum] : ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) @ ( V10q2 @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
& ( V2Psi2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) @ V1i @ V10q2 ) ) ) )
<=> ? [V12q1: tyop_2Enum_2Enum > A_27b1,V13q2: tyop_2Enum_2Enum > A_27b2] :
( ( V7Phi__I1 @ ( V12q1 @ V0t0 ) )
& ( V6Phi__I2 @ ( V13q2 @ V0t0 ) )
& ! [V14t: tyop_2Enum_2Enum] :
( ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) @ ( V12q1 @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) )
& ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) @ ( V13q2 @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) ) )
& ( V3Psi1 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) @ V1i @ V12q1 ) )
& ( V2Psi2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) @ V1i @ V13q2 ) ) ) ) ).
thf(thm_2EOmega__Automata_2EOMEGA__DISJ__CLOSURE,axiom,
! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27a,V2Psi2: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) ) > $o,V3Psi1: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) ) > $o,V4Phi__R2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V5Phi__R1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V6Phi__I2: A_27b2 > $o,V7Phi__I1: A_27b1 > $o] :
( ( ? [V8q1: tyop_2Enum_2Enum > A_27b1] :
( ( V7Phi__I1 @ ( V8q1 @ V0t0 ) )
& ! [V9t: tyop_2Enum_2Enum] : ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) @ ( V8q1 @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) )
& ( V3Psi1 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) @ V1i @ V8q1 ) ) )
| ? [V10q2: tyop_2Enum_2Enum > A_27b2] :
( ( V6Phi__I2 @ ( V10q2 @ V0t0 ) )
& ! [V11t: tyop_2Enum_2Enum] : ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) @ ( V10q2 @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
& ( V2Psi2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) @ V1i @ V10q2 ) ) ) )
<=> ? [V12p: tyop_2Enum_2Enum > $o,V13q1: tyop_2Enum_2Enum > A_27b1,V14q2: tyop_2Enum_2Enum > A_27b2] :
( ( ( ( (~) @ ( V12p @ V0t0 ) )
& ( V7Phi__I1 @ ( V13q1 @ V0t0 ) ) )
| ( ( V12p @ V0t0 )
& ( V6Phi__I2 @ ( V14q2 @ V0t0 ) ) ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V13q1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ( ( ( (~) @ ( V12p @ V0t0 ) )
& ( V3Psi1 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b1 ) @ V1i @ V13q1 ) ) )
| ( ( V12p @ V0t0 )
& ( V2Psi2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b2 ) @ V1i @ V14q2 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__G,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ! [V3t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
<=> ? [V4t: tyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( ( ! [V5t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
& ! [V6t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
<=> ! [V7t: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
& ( ( ! [V8t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
| ! [V9t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ? [V10p: tyop_2Enum_2Enum > $o,V11q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V10p @ V0t0 ) )
& ( (~) @ ( V11q @ V0t0 ) )
& ! [V12t: tyop_2Enum_2Enum] :
( ( ( V10p @ ( c_2Earithmetic_2E_2B @ V12t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V10p @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) )
& ( ( V11q @ ( c_2Earithmetic_2E_2B @ V12t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V11q @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) ) )
& ! [V13t: tyop_2Enum_2Enum] :
( ( (~) @ ( V10p @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
| ( (~) @ ( V11q @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__F,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ? [V3t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
<=> ! [V4t: tyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( ( ? [V5t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
| ? [V6t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
<=> ? [V7t: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
& ( ( ? [V8t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
& ? [V9t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ? [V10p: tyop_2Enum_2Enum > $o,V11q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V10p @ V0t0 ) )
& ( (~) @ ( V11q @ V0t0 ) )
& ! [V12t: tyop_2Enum_2Enum] :
( ( ( V10p @ ( c_2Earithmetic_2E_2B @ V12t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V10p @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( V2a @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) )
& ( ( V11q @ ( c_2Earithmetic_2E_2B @ V12t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
<=> ( ( V11q @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V12t @ V0t0 ) ) ) ) )
& ? [V13t: tyop_2Enum_2Enum] :
( ( V10p @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( V11q @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__FG,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ? [V3t1: tyop_2Enum_2Enum] :
! [V4t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V3t1 @ ( c_2Earithmetic_2E_2B @ V4t2 @ V0t0 ) ) ) )
<=> ! [V5t1: tyop_2Enum_2Enum] :
? [V6t2: tyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ( ? [V7t1: tyop_2Enum_2Enum] :
! [V8t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V7t1 @ ( c_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
& ? [V9t1: tyop_2Enum_2Enum] :
! [V10t2: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V9t1 @ ( c_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) )
<=> ? [V11t1: tyop_2Enum_2Enum] :
! [V12t2: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) )
& ( ( ? [V13t1: tyop_2Enum_2Enum] :
! [V14t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V13t1 @ ( c_2Earithmetic_2E_2B @ V14t2 @ V0t0 ) ) )
| ? [V15t1: tyop_2Enum_2Enum] :
! [V16t2: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
<=> ? [V17q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V17q @ V0t0 ) )
& ! [V18t: tyop_2Enum_2Enum] :
( ( V17q @ ( c_2Earithmetic_2E_2B @ V18t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ebool_2ECOND @ $o @ ( V17q @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( c_2Ebool_2E_7E @ ( V2a @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) )
& ? [V19t1: tyop_2Enum_2Enum] :
! [V20t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V17q @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOOLEAN__CLOSURE__GF,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( (~)
@ ! [V3t1: tyop_2Enum_2Enum] :
? [V4t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V3t1 @ ( c_2Earithmetic_2E_2B @ V4t2 @ V0t0 ) ) ) )
<=> ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ( ! [V7t1: tyop_2Enum_2Enum] :
? [V8t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V7t1 @ ( c_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
| ! [V9t1: tyop_2Enum_2Enum] :
? [V10t2: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V9t1 @ ( c_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) )
<=> ! [V11t1: tyop_2Enum_2Enum] :
? [V12t2: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) )
& ( ( ! [V13t1: tyop_2Enum_2Enum] :
? [V14t2: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V13t1 @ ( c_2Earithmetic_2E_2B @ V14t2 @ V0t0 ) ) )
& ! [V15t1: tyop_2Enum_2Enum] :
? [V16t2: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
<=> ? [V17q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V17q @ V0t0 ) )
& ! [V18t: tyop_2Enum_2Enum] :
( ( V17q @ ( c_2Earithmetic_2E_2B @ V18t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= ( c_2Ebool_2ECOND @ $o @ ( V17q @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( c_2Ebool_2E_7E @ ( V1b @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) )
& ! [V19t1: tyop_2Enum_2Enum] :
? [V20t2: tyop_2Enum_2Enum] :
( ( V17q @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__G,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( ! [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( V3q @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ? [V5t: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) )
& ( ! [V6t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) )
<=> ? [V7q: tyop_2Enum_2Enum > $o] :
( ( V7q @ V0t0 )
& ! [V8t: tyop_2Enum_2Enum] :
( ( V7q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
<=> ( ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) )
& ( V1a @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) )
& ? [V9t1: tyop_2Enum_2Enum] :
! [V10t2: tyop_2Enum_2Enum] : ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ ( c_2Earithmetic_2E_2B @ V10t2 @ V0t0 ) ) ) ) )
& ( ! [V11t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
<=> ? [V12q: tyop_2Enum_2Enum > $o] :
( ( V12q @ V0t0 )
& ! [V13t: tyop_2Enum_2Enum] :
( ( V12q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
<=> ( ( V12q @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( V1a @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) )
& ! [V14t1: tyop_2Enum_2Enum] :
? [V15t2: tyop_2Enum_2Enum] : ( V12q @ ( c_2Earithmetic_2E_2B @ V14t1 @ ( c_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__F,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( ? [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
<=> ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V1a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) )
& ( ? [V7t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) )
<=> ? [V8q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V8q @ V0t0 ) )
& ! [V9t: tyop_2Enum_2Enum] :
( ( V8q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) )
<=> ( ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) )
| ( V1a @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) )
& ! [V10t1: tyop_2Enum_2Enum] :
? [V11t2: tyop_2Enum_2Enum] : ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBOREL__HIERARCHY__FG,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( ? [V2t1: tyop_2Enum_2Enum] :
! [V3t2: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t1 @ ( c_2Earithmetic_2E_2B @ V3t2 @ V0t0 ) ) )
<=> ? [V4q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V4q @ V0t0 ) )
& ! [V5t: tyop_2Enum_2Enum] :
( ( V4q @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
=> ( ( V1a @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) )
& ( V4q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) )
& ? [V6t: tyop_2Enum_2Enum] : ( V4q @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) )
& ( ? [V7t1: tyop_2Enum_2Enum] :
! [V8t2: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V7t1 @ ( c_2Earithmetic_2E_2B @ V8t2 @ V0t0 ) ) )
<=> ? [V9p: tyop_2Enum_2Enum > $o,V10q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V9p @ V0t0 ) )
& ( (~) @ ( V10q @ V0t0 ) )
& ! [V11t: tyop_2Enum_2Enum] :
( ( ( V9p @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
=> ( V9p @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
& ( ( V9p @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
=> ( ( V9p @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
| ( (~) @ ( V10q @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) )
& ( ( V10q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
<=> ( ( ( V9p @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
& ( (~) @ ( V10q @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) )
& ( (~) @ ( V1a @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) )
| ( ( V9p @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) )
& ( V10q @ ( c_2Earithmetic_2E_2B @ V11t @ V0t0 ) ) ) ) ) )
& ! [V12t1: tyop_2Enum_2Enum] :
? [V13t2: tyop_2Enum_2Enum] :
( ( V9p @ ( c_2Earithmetic_2E_2B @ V12t1 @ ( c_2Earithmetic_2E_2B @ V13t2 @ V0t0 ) ) )
& ( (~) @ ( V10q @ ( c_2Earithmetic_2E_2B @ V12t1 @ ( c_2Earithmetic_2E_2B @ V13t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ETEMP__OPS__DEFS__TO__OMEGA,axiom,
! [V0l: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( ( V0l
= ( c_2ETemporal__Logic_2ENEXT @ V2a ) )
<=> ( c_2Ebool_2ET
& ! [V3t: tyop_2Enum_2Enum] :
( ( V0l @ V3t )
= ( V2a @ ( c_2Enum_2ESUC @ V3t ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2EALWAYS @ V2a ) )
<=> ( c_2Ebool_2ET
& ! [V4t: tyop_2Enum_2Enum] :
( ( V0l @ V4t )
<=> ( ( V2a @ V4t )
& ( V0l @ ( c_2Enum_2ESUC @ V4t ) ) ) )
& ! [V5t1: tyop_2Enum_2Enum] :
? [V6t2: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V5t1 @ V6t2 ) )
=> ( V0l @ ( c_2Earithmetic_2E_2B @ V5t1 @ V6t2 ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
<=> ( c_2Ebool_2ET
& ! [V7t: tyop_2Enum_2Enum] :
( ( V0l @ V7t )
<=> ( ( V2a @ V7t )
| ( V0l @ ( c_2Enum_2ESUC @ V7t ) ) ) )
& ! [V8t1: tyop_2Enum_2Enum] :
? [V9t2: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Earithmetic_2E_2B @ V8t1 @ V9t2 ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V8t1 @ V9t2 ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V10t: tyop_2Enum_2Enum] :
( ( V0l @ V10t )
<=> ( ( (~) @ ( V1b @ V10t ) )
=> ( ( V2a @ V10t )
& ( V0l @ ( c_2Enum_2ESUC @ V10t ) ) ) ) )
& ! [V11t1: tyop_2Enum_2Enum] :
? [V12t2: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) )
=> ( ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V11t1 @ V12t2 ) ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V13t: tyop_2Enum_2Enum] :
( ( V0l @ V13t )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V13t ) @ ( V2a @ V13t ) @ ( V0l @ ( c_2Enum_2ESUC @ V13t ) ) ) )
& ! [V14t1: tyop_2Enum_2Enum] :
? [V15t2: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Earithmetic_2E_2B @ V14t1 @ V15t2 ) )
=> ( V1b @ ( c_2Earithmetic_2E_2B @ V14t1 @ V15t2 ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V16t: tyop_2Enum_2Enum] :
( ( V0l @ V16t )
<=> ( ( (~) @ ( V1b @ V16t ) )
& ( ( V2a @ V16t )
| ( V0l @ ( c_2Enum_2ESUC @ V16t ) ) ) ) )
& ! [V17t1: tyop_2Enum_2Enum] :
? [V18t2: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V19t: tyop_2Enum_2Enum] :
( ( V0l @ V19t )
<=> ( ( (~) @ ( V1b @ V19t ) )
=> ( ( V2a @ V19t )
& ( V0l @ ( c_2Enum_2ESUC @ V19t ) ) ) ) )
& ! [V20t1: tyop_2Enum_2Enum] :
? [V21t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V0l @ ( c_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) )
=> ( ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V20t1 @ V21t2 ) ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V22t: tyop_2Enum_2Enum] :
( ( V0l @ V22t )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V22t ) @ ( V2a @ V22t ) @ ( V0l @ ( c_2Enum_2ESUC @ V22t ) ) ) )
& ! [V23t1: tyop_2Enum_2Enum] :
? [V24t2: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Earithmetic_2E_2B @ V23t1 @ V24t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V23t1 @ V24t2 ) ) ) ) )
& ( ( V0l
= ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
<=> ( c_2Ebool_2ET
& ! [V25t: tyop_2Enum_2Enum] :
( ( V0l @ V25t )
<=> ( ( (~) @ ( V1b @ V25t ) )
& ( ( V2a @ V25t )
| ( V0l @ ( c_2Enum_2ESUC @ V25t ) ) ) ) )
& ! [V26t1: tyop_2Enum_2Enum] :
? [V27t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V0l @ ( c_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) ) )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V26t1 @ V27t2 ) ) ) ) ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPNEXT @ V2a ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V28t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V28t ) )
= ( V2a @ V28t ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPSNEXT @ V2a ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V29t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V29t ) )
= ( V2a @ V29t ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V30t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V30t ) )
<=> ( ( V2a @ V30t )
& ( V0l @ V30t ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V31t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V31t ) )
<=> ( ( V2a @ V31t )
| ( V0l @ V31t ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V32t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V32t ) )
<=> ( ( V1b @ V32t )
| ( ( V2a @ V32t )
& ( V0l @ V32t ) ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V33t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V33t ) )
<=> ( ( ( V2a @ V33t )
& ( V1b @ V33t ) )
| ( ( (~) @ ( V1b @ V33t ) )
& ( V0l @ V33t ) ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2EF )
& ! [V34t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V34t ) )
<=> ( ( (~) @ ( V1b @ V34t ) )
& ( ( V2a @ V34t )
| ( V0l @ V34t ) ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V35t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V35t ) )
<=> ( ( V1b @ V35t )
| ( ( V2a @ V35t )
& ( V0l @ V35t ) ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V36t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V36t ) )
<=> ( ( ( V2a @ V36t )
& ( V1b @ V36t ) )
| ( ( (~) @ ( V1b @ V36t ) )
& ( V0l @ V36t ) ) ) )
& c_2Ebool_2ET ) )
& ( ( V0l
= ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) )
<=> ( ( ( V0l @ c_2Enum_2E0 )
= c_2Ebool_2ET )
& ! [V37t: tyop_2Enum_2Enum] :
( ( V0l @ ( c_2Enum_2ESUC @ V37t ) )
<=> ( ( (~) @ ( V1b @ V37t ) )
& ( ( V2a @ V37t )
| ( V0l @ V37t ) ) ) )
& c_2Ebool_2ET ) ) ) ).
thf(thm_2EOmega__Automata_2EAUTOMATON__TEMP__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0phi: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o,V3Phi__R2: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27b ) @ ( tyop_2Enum_2Enum > A_27a ) ) > $o,V4Phi__R1: ( tyop_2Enum_2Enum > A_27a ) > $o,V5Phi__I2: ( tyop_2Enum_2Enum > A_27b ) > $o,V6Phi__I1: ( tyop_2Enum_2Enum > A_27a ) > $o,V7Phi__F: ( tyop_2Epair_2Eprod @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b ) ) > $o,V8Phi: ( tyop_2Enum_2Enum > $o ) > $o] :
( ( ? [V9q1: tyop_2Enum_2Enum > A_27a] :
( ( V6Phi__I1 @ V9q1 )
& ( V4Phi__R1 @ V9q1 )
& ? [V10q2: tyop_2Enum_2Enum > A_27b] :
( ( V5Phi__I2 @ V10q2 )
& ( V3Phi__R2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27b ) @ ( tyop_2Enum_2Enum > A_27a ) @ V10q2 @ V9q1 ) )
& ( V7Phi__F @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b ) @ V9q1 @ V10q2 ) ) ) )
<=> ? [V11q1: tyop_2Enum_2Enum > A_27a,V12q2: tyop_2Enum_2Enum > A_27b] :
( ( V6Phi__I1 @ V11q1 )
& ( V5Phi__I2 @ V12q2 )
& ( V4Phi__R1 @ V11q1 )
& ( V3Phi__R2 @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27b ) @ ( tyop_2Enum_2Enum > A_27a ) @ V12q2 @ V11q1 ) )
& ( V7Phi__F @ ( c_2Epair_2E_2C @ ( tyop_2Enum_2Enum > A_27a ) @ ( tyop_2Enum_2Enum > A_27b ) @ V11q1 @ V12q2 ) ) ) )
& ( ( V8Phi @ ( c_2ETemporal__Logic_2ENEXT @ V0phi ) )
<=> ? [V13q0: tyop_2Enum_2Enum > $o,V14q1: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( V13q0 @ V15t )
= ( V0phi @ V15t ) )
& ( ( V14q1 @ V15t )
= ( V13q0 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V8Phi @ V14q1 ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPNEXT @ V0phi ) )
<=> ? [V16q: tyop_2Enum_2Enum > $o] :
( ( V16q @ c_2Enum_2E0 )
& ! [V17t: tyop_2Enum_2Enum] :
( ( V16q @ ( c_2Earithmetic_2E_2B @ V17t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( V0phi @ V17t ) )
& ( V8Phi @ V16q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ V0phi ) )
<=> ? [V18q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V18q @ c_2Enum_2E0 ) )
& ! [V19t: tyop_2Enum_2Enum] :
( ( V18q @ ( c_2Earithmetic_2E_2B @ V19t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
= ( V0phi @ V19t ) )
& ( V8Phi @ V18q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPALWAYS @ V2a ) ) )
<=> ? [V20q: tyop_2Enum_2Enum > $o] :
( ( V20q @ c_2Enum_2E0 )
& ! [V21t: tyop_2Enum_2Enum] :
( ( V20q @ ( c_2Earithmetic_2E_2B @ V21t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V2a @ V21t )
& ( V20q @ V21t ) ) )
& ( V8Phi @ V20q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPEVENTUAL @ V2a ) ) )
<=> ? [V22q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V22q @ c_2Enum_2E0 ) )
& ! [V23t: tyop_2Enum_2Enum] :
( ( V22q @ ( c_2Earithmetic_2E_2B @ V23t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V2a @ V23t )
| ( V22q @ V23t ) ) )
& ( V8Phi @ V22q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSUNTIL @ V2a @ V1b ) ) )
<=> ? [V24q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V24q @ c_2Enum_2E0 ) )
& ! [V25t: tyop_2Enum_2Enum] :
( ( V24q @ ( c_2Earithmetic_2E_2B @ V25t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V1b @ V25t )
| ( ( V2a @ V25t )
& ( V24q @ V25t ) ) ) )
& ( V8Phi @ V24q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSWHEN @ V2a @ V1b ) ) )
<=> ? [V26q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V26q @ c_2Enum_2E0 ) )
& ! [V27t: tyop_2Enum_2Enum] :
( ( V26q @ ( c_2Earithmetic_2E_2B @ V27t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( ( V2a @ V27t )
& ( V1b @ V27t ) )
| ( ( (~) @ ( V1b @ V27t ) )
& ( V26q @ V27t ) ) ) )
& ( V8Phi @ V26q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPSNEXT @ ( c_2EPast__Temporal__Logic_2EPSBEFORE @ V2a @ V1b ) ) )
<=> ? [V28q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V28q @ c_2Enum_2E0 ) )
& ! [V29t: tyop_2Enum_2Enum] :
( ( V28q @ ( c_2Earithmetic_2E_2B @ V29t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( (~) @ ( V1b @ V29t ) )
& ( ( V2a @ V29t )
| ( V28q @ V29t ) ) ) )
& ( V8Phi @ V28q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPUNTIL @ V2a @ V1b ) ) )
<=> ? [V30q: tyop_2Enum_2Enum > $o] :
( ( V30q @ c_2Enum_2E0 )
& ! [V31t: tyop_2Enum_2Enum] :
( ( V30q @ ( c_2Earithmetic_2E_2B @ V31t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( V1b @ V31t )
| ( ( V2a @ V31t )
& ( V30q @ V31t ) ) ) )
& ( V8Phi @ V30q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPWHEN @ V2a @ V1b ) ) )
<=> ? [V32q: tyop_2Enum_2Enum > $o] :
( ( V32q @ c_2Enum_2E0 )
& ! [V33t: tyop_2Enum_2Enum] :
( ( V32q @ ( c_2Earithmetic_2E_2B @ V33t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( ( V2a @ V33t )
& ( V1b @ V33t ) )
| ( ( (~) @ ( V1b @ V33t ) )
& ( V32q @ V33t ) ) ) )
& ( V8Phi @ V32q ) ) )
& ( ( V8Phi @ ( c_2EPast__Temporal__Logic_2EPNEXT @ ( c_2EPast__Temporal__Logic_2EPBEFORE @ V2a @ V1b ) ) )
<=> ? [V34q: tyop_2Enum_2Enum > $o] :
( ( V34q @ c_2Enum_2E0 )
& ! [V35t: tyop_2Enum_2Enum] :
( ( V34q @ ( c_2Earithmetic_2E_2B @ V35t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) )
<=> ( ( (~) @ ( V1b @ V35t ) )
& ( ( V2a @ V35t )
| ( V34q @ V35t ) ) ) )
& ( V8Phi @ V34q ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__TRANSLATION,axiom,
! [V0phi: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o,V3Phi: ( tyop_2Enum_2Enum > $o ) > $o] :
( ( ( V3Phi @ ( c_2ETemporal__Logic_2ENEXT @ V0phi ) )
<=> ? [V4q0: tyop_2Enum_2Enum > $o,V5q1: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V6t: tyop_2Enum_2Enum] :
( ( ( V4q0 @ V6t )
= ( V0phi @ V6t ) )
& ( ( V5q1 @ V6t )
= ( V4q0 @ ( c_2Earithmetic_2E_2B @ V6t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V3Phi @ V5q1 ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2EALWAYS @ V2a ) )
<=> ? [V7q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V8t: tyop_2Enum_2Enum] :
( ( V7q @ V8t )
<=> ( ( V2a @ V8t )
& ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V9t1: tyop_2Enum_2Enum] :
? [V10t2: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) )
=> ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) )
& ( V3Phi @ V7q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2EEVENTUAL @ V2a ) )
<=> ? [V11q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V12t: tyop_2Enum_2Enum] :
( ( V11q @ V12t )
<=> ( ( V2a @ V12t )
| ( V11q @ ( c_2Earithmetic_2E_2B @ V12t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V13t1: tyop_2Enum_2Enum] :
? [V14t2: tyop_2Enum_2Enum] :
( ( V11q @ ( c_2Earithmetic_2E_2B @ V13t1 @ V14t2 ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V13t1 @ V14t2 ) ) )
& ( V3Phi @ V11q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) )
<=> ? [V15q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V16t: tyop_2Enum_2Enum] :
( ( V15q @ V16t )
<=> ( ( V1b @ V16t )
| ( ( V2a @ V16t )
& ( V15q @ ( c_2Earithmetic_2E_2B @ V16t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V17t1: tyop_2Enum_2Enum] :
? [V18t2: tyop_2Enum_2Enum] :
( ( V15q @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) )
=> ( ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V17t1 @ V18t2 ) ) ) )
& ( V3Phi @ V15q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
<=> ? [V19q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V20t: tyop_2Enum_2Enum] :
( ( V19q @ V20t )
<=> ( ( V1b @ V20t )
| ( ( V2a @ V20t )
& ( V19q @ ( c_2Earithmetic_2E_2B @ V20t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V21t1: tyop_2Enum_2Enum] :
? [V22t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V19q @ ( c_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) )
=> ( ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V21t1 @ V22t2 ) ) ) )
& ( V3Phi @ V19q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) )
<=> ? [V23q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V24t: tyop_2Enum_2Enum] :
( ( V23q @ V24t )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V24t ) @ ( V2a @ V24t ) @ ( V23q @ ( c_2Earithmetic_2E_2B @ V24t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V25t1: tyop_2Enum_2Enum] :
? [V26t2: tyop_2Enum_2Enum] :
( ( V23q @ ( c_2Earithmetic_2E_2B @ V25t1 @ V26t2 ) )
=> ( V1b @ ( c_2Earithmetic_2E_2B @ V25t1 @ V26t2 ) ) )
& ( V3Phi @ V23q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
<=> ? [V27q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V28t: tyop_2Enum_2Enum] :
( ( V27q @ V28t )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V28t ) @ ( V2a @ V28t ) @ ( V27q @ ( c_2Earithmetic_2E_2B @ V28t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ! [V29t1: tyop_2Enum_2Enum] :
? [V30t2: tyop_2Enum_2Enum] :
( ( V27q @ ( c_2Earithmetic_2E_2B @ V29t1 @ V30t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V29t1 @ V30t2 ) ) )
& ( V3Phi @ V27q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) )
<=> ? [V31q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V32t: tyop_2Enum_2Enum] :
( ( V31q @ V32t )
<=> ( ( (~) @ ( V1b @ V32t ) )
& ( ( V2a @ V32t )
| ( V31q @ ( c_2Earithmetic_2E_2B @ V32t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V33t1: tyop_2Enum_2Enum] :
? [V34t2: tyop_2Enum_2Enum] :
( ( V31q @ ( c_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V33t1 @ V34t2 ) ) ) )
& ( V3Phi @ V31q ) ) )
& ( ( V3Phi @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) )
<=> ? [V35q: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ET
& ! [V36t: tyop_2Enum_2Enum] :
( ( V35q @ V36t )
<=> ( ( (~) @ ( V1b @ V36t ) )
& ( ( V2a @ V36t )
| ( V35q @ ( c_2Earithmetic_2E_2B @ V36t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V37t1: tyop_2Enum_2Enum] :
? [V38t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V35q @ ( c_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) ) )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V37t1 @ V38t2 ) ) ) )
& ( V3Phi @ V35q ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__CONJ__CLOSURE,axiom,
! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27a,V2Psi2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V3Psi1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V4Phi__R2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V5Phi__R1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V6Phi__I2: A_27b2 > $o,V7Phi__I1: A_27b1 > $o] :
( ( ? [V8q1: tyop_2Enum_2Enum > A_27b1] :
( ( V7Phi__I1 @ ( V8q1 @ V0t0 ) )
& ! [V9t: tyop_2Enum_2Enum] : ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) @ ( V8q1 @ ( c_2Earithmetic_2E_2B @ V9t @ V0t0 ) ) ) )
& ? [V10t1: tyop_2Enum_2Enum] :
! [V11t2: tyop_2Enum_2Enum] : ( V3Psi1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) @ ( V8q1 @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V0t0 ) ) ) ) ) )
& ? [V12q2: tyop_2Enum_2Enum > A_27b2] :
( ( V6Phi__I2 @ ( V12q2 @ V0t0 ) )
& ! [V13t: tyop_2Enum_2Enum] : ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) @ ( V12q2 @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) )
& ? [V14t1: tyop_2Enum_2Enum] :
! [V15t2: tyop_2Enum_2Enum] : ( V2Psi2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V14t1 @ ( c_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) @ ( V12q2 @ ( c_2Earithmetic_2E_2B @ V14t1 @ ( c_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) )
<=> ? [V16q1: tyop_2Enum_2Enum > A_27b1,V17q2: tyop_2Enum_2Enum > A_27b2] :
( ( V7Phi__I1 @ ( V16q1 @ V0t0 ) )
& ( V6Phi__I2 @ ( V17q2 @ V0t0 ) )
& ! [V18t: tyop_2Enum_2Enum] :
( ( V5Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( V16q1 @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) )
& ( V4Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) @ ( V17q2 @ ( c_2Earithmetic_2E_2B @ V18t @ V0t0 ) ) ) ) )
& ? [V19t1: tyop_2Enum_2Enum] :
! [V20t2: tyop_2Enum_2Enum] :
( ( V3Psi1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) @ ( V16q1 @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) )
& ( V2Psi2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V1i @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) @ ( V17q2 @ ( c_2Earithmetic_2E_2B @ V19t1 @ ( c_2Earithmetic_2E_2B @ V20t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__DISJ__CLOSURE,axiom,
! [A_27a: $tType,A_27b1: $tType,A_27b2: $tType,V0t0: tyop_2Enum_2Enum,V1t: tyop_2Enum_2Enum,V2i: tyop_2Enum_2Enum > A_27a,V3Psi2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V4Psi1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V5Phi__R2: ( tyop_2Epair_2Eprod @ A_27a @ A_27b2 ) > $o,V6Phi__R1: ( tyop_2Epair_2Eprod @ A_27a @ A_27b1 ) > $o,V7Phi__I2: A_27b2 > $o,V8Phi__I1: A_27b1 > $o] :
( ( ? [V9q1: tyop_2Enum_2Enum > A_27b1] :
( ( V8Phi__I1 @ ( V9q1 @ V0t0 ) )
& ! [V10t: tyop_2Enum_2Enum] : ( V6Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) @ ( V9q1 @ ( c_2Earithmetic_2E_2B @ V10t @ V0t0 ) ) ) )
& ? [V11t1: tyop_2Enum_2Enum] :
! [V12t2: tyop_2Enum_2Enum] : ( V4Psi1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) @ ( V9q1 @ ( c_2Earithmetic_2E_2B @ V11t1 @ ( c_2Earithmetic_2E_2B @ V12t2 @ V0t0 ) ) ) ) ) )
| ? [V13q2: tyop_2Enum_2Enum > A_27b2] :
( ( V7Phi__I2 @ ( V13q2 @ V0t0 ) )
& ! [V14t: tyop_2Enum_2Enum] : ( V5Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) @ ( V13q2 @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) )
& ? [V15t1: tyop_2Enum_2Enum] :
! [V16t2: tyop_2Enum_2Enum] : ( V3Psi2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) @ ( V13q2 @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) )
<=> ? [V17p: tyop_2Enum_2Enum > $o,V18q1: tyop_2Enum_2Enum > A_27b1,V19q2: tyop_2Enum_2Enum > A_27b2] :
( ( ( ( (~) @ ( V17p @ V0t0 ) )
& ( V8Phi__I1 @ ( V18q1 @ V0t0 ) ) )
| ( ( V17p @ V0t0 )
& ( V7Phi__I2 @ ( V19q2 @ V0t0 ) ) ) )
& ! [V20t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V17p @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) )
& ( V6Phi__R1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) @ ( V18q1 @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) )
& ( (~) @ ( V17p @ ( c_2Earithmetic_2E_2B @ V20t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V17p @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) )
& ( V5Phi__R2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) @ ( V19q2 @ ( c_2Earithmetic_2E_2B @ V20t @ V0t0 ) ) ) )
& ( V17p @ ( c_2Earithmetic_2E_2B @ V20t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V21t1: tyop_2Enum_2Enum] :
! [V22t2: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V17p @ ( c_2Earithmetic_2E_2B @ V1t @ V0t0 ) ) )
& ( V4Psi1 @ ( c_2Epair_2E_2C @ A_27a @ A_27b1 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V21t1 @ ( c_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) @ ( V18q1 @ ( c_2Earithmetic_2E_2B @ V21t1 @ ( c_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) )
| ( ( V17p @ ( c_2Earithmetic_2E_2B @ V1t @ V0t0 ) )
& ( V3Psi2 @ ( c_2Epair_2E_2C @ A_27a @ A_27b2 @ ( V2i @ ( c_2Earithmetic_2E_2B @ V21t1 @ ( c_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) @ ( V19q2 @ ( c_2Earithmetic_2E_2B @ V21t1 @ ( c_2Earithmetic_2E_2B @ V22t2 @ V0t0 ) ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__NEXT__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1i: tyop_2Enum_2Enum > A_27a,V2c: A_27b,V3Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V4Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V6t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V7q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V5Phi__I @ ( V7q @ V6t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V8t: tyop_2Enum_2Enum] : ( V4Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V1i @ ( c_2Earithmetic_2E_2B @ V8t @ V6t0 ) ) @ ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ V6t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V9t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V10t2: tyop_2Enum_2Enum] : ( V3Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V1i @ ( c_2Earithmetic_2E_2B @ V9t1 @ ( c_2Earithmetic_2E_2B @ V10t2 @ V6t0 ) ) ) @ ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ ( c_2Earithmetic_2E_2B @ V10t2 @ V6t0 ) ) ) ) ) ) ) ) ) )
@ V0t0 )
<=> ? [V11p: tyop_2Enum_2Enum > $o,V12q: tyop_2Enum_2Enum > A_27b] :
( ( ( V11p @ V0t0 )
= c_2Ebool_2EF )
& ( ( V12q @ V0t0 )
= V2c )
& ! [V13t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V11p @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) )
& ( ( V12q @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
= V2c )
& ( V11p @ ( c_2Earithmetic_2E_2B @ V13t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V5Phi__I @ ( V12q @ ( c_2Earithmetic_2E_2B @ V13t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V11p @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) )
& ( V4Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V1i @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) @ ( V12q @ ( c_2Earithmetic_2E_2B @ V13t @ V0t0 ) ) ) )
& ( V11p @ ( c_2Earithmetic_2E_2B @ V13t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V14t1: tyop_2Enum_2Enum] :
! [V15t2: tyop_2Enum_2Enum] : ( V3Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V1i @ ( c_2Earithmetic_2E_2B @ V14t1 @ ( c_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) @ ( V12q @ ( c_2Earithmetic_2E_2B @ V14t1 @ ( c_2Earithmetic_2E_2B @ V15t2 @ V0t0 ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SUNTIL__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1phi
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V0t0 )
<=> ? [V12p: tyop_2Enum_2Enum > $o,V13q: tyop_2Enum_2Enum > A_27b] :
( ( c_2Ebool_2ECOND @ $o @ ( V12p @ V0t0 ) @ ( V6Phi__I @ ( V13q @ V0t0 ) ) @ ( c_2Emin_2E_3D @ A_27b @ ( V13q @ V0t0 ) @ V3c ) )
& ! [V14t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
= V3c )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
= V3c )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V6Phi__I @ ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) @ ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) )
& ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V15t1: tyop_2Enum_2Enum] :
! [V16t2: tyop_2Enum_2Enum] :
( ( V12p @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) )
& ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) @ ( V13q @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__UNTIL__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1phi
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V0t0 )
<=> ? [V12p: tyop_2Enum_2Enum > $o,V13q: tyop_2Enum_2Enum > A_27b] :
( ( c_2Ebool_2ECOND @ $o @ ( V12p @ V0t0 ) @ ( V6Phi__I @ ( V13q @ V0t0 ) ) @ ( c_2Emin_2E_3D @ A_27b @ ( V13q @ V0t0 ) @ V3c ) )
& ! [V14t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
= V3c )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) )
& ( ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
= V3c )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V6Phi__I @ ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) @ ( V13q @ ( c_2Earithmetic_2E_2B @ V14t @ V0t0 ) ) ) )
& ( V12p @ ( c_2Earithmetic_2E_2B @ V14t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V15t1: tyop_2Enum_2Enum] :
! [V16t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V12p @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) )
| ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) @ ( V13q @ ( c_2Earithmetic_2E_2B @ V15t1 @ ( c_2Earithmetic_2E_2B @ V16t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SBEFORE__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V1phi
@ V0t0 )
<=> ? [V12p1: tyop_2Enum_2Enum > $o,V13p2: tyop_2Enum_2Enum > $o,V14q: tyop_2Enum_2Enum > A_27b] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( V14q @ V0t0 )
= V3c ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ V0t0 ) ) ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: tyop_2Enum_2Enum] :
! [V17t2: tyop_2Enum_2Enum] :
( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) )
& ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__BEFORE__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V1phi
@ V0t0 )
<=> ? [V12p1: tyop_2Enum_2Enum > $o,V13p2: tyop_2Enum_2Enum > $o,V14q: tyop_2Enum_2Enum > A_27b] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( V14q @ V0t0 )
= V3c ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ V0t0 ) ) ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: tyop_2Enum_2Enum] :
! [V17t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) )
| ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__SWHEN__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V1phi
@ V0t0 )
<=> ? [V12p1: tyop_2Enum_2Enum > $o,V13p2: tyop_2Enum_2Enum > $o,V14q: tyop_2Enum_2Enum > A_27b] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( V14q @ V0t0 )
= V3c ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ V0t0 ) ) ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: tyop_2Enum_2Enum] :
! [V17t2: tyop_2Enum_2Enum] :
( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) )
& ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ECO__BUECHI__WHEN__CLOSURE,axiom,
! [A_27a: $tType,A_27b: $tType,V0t0: tyop_2Enum_2Enum,V1phi: tyop_2Enum_2Enum > $o,V2i: tyop_2Enum_2Enum > A_27a,V3c: A_27b,V4Psi: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V5Phi__R: ( tyop_2Epair_2Eprod @ A_27a @ A_27b ) > $o,V6Phi__I: A_27b > $o] :
( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V7t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ ( tyop_2Enum_2Enum > A_27b )
@ ^ [V8q: tyop_2Enum_2Enum > A_27b] :
( c_2Ebool_2E_2F_5C @ ( V6Phi__I @ ( V8q @ V7t0 ) )
@ ( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V9t: tyop_2Enum_2Enum] : ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V9t @ V7t0 ) ) ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V10t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V11t2: tyop_2Enum_2Enum] : ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) @ ( V8q @ ( c_2Earithmetic_2E_2B @ V10t1 @ ( c_2Earithmetic_2E_2B @ V11t2 @ V7t0 ) ) ) ) ) ) ) ) ) )
@ V1phi
@ V0t0 )
<=> ? [V12p1: tyop_2Enum_2Enum > $o,V13p2: tyop_2Enum_2Enum > $o,V14q: tyop_2Enum_2Enum > A_27b] :
( ( ( ( (~) @ ( V12p1 @ V0t0 ) )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( ( V14q @ V0t0 )
= V3c ) )
| ( ( V12p1 @ V0t0 )
& ( (~) @ ( V13p2 @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ V0t0 ) ) ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
= V3c ) )
| ( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
= V3c )
& ( (~) @ ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( (~) @ ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V1phi @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V6Phi__I @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) )
| ( ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) )
& ( V5Phi__R @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V15t @ V0t0 ) ) ) )
& ( V12p1 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) )
& ( V13p2 @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ? [V16t1: tyop_2Enum_2Enum] :
! [V17t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V12p1 @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) )
| ( V4Psi @ ( c_2Epair_2E_2C @ A_27a @ A_27b @ ( V2i @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) @ ( V14q @ ( c_2Earithmetic_2E_2B @ V16t1 @ ( c_2Earithmetic_2E_2B @ V17t2 @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ENEXT__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ V1a @ V0t0 )
<=> ? [V2p: tyop_2Enum_2Enum > $o,V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V2p @ V0t0 ) )
& ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V2p @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESUNTIL__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EUNTIL__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESBEFORE__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBEFORE__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2ESWHEN__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] : ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EWHEN__AS__CO__BUECHI,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( V3q @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
| ( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) )
| ( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ ( c_2Earithmetic_2E_2B @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) @ V0t0 ) ) ) ) )
& ? [V5t1: tyop_2Enum_2Enum] :
! [V6t2: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) )
| ( V3q @ ( c_2Earithmetic_2E_2B @ V5t1 @ ( c_2Earithmetic_2E_2B @ V6t2 @ V0t0 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PERIODIC__MODEL,axiom,
! [A_27a: $tType,A_27state: $tType,V0TransRel: ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) > $o,V1InitState: A_27state > $o,V2Accept: A_27state > $o] :
( ! [V3s: tyop_2Enum_2Enum > A_27state] :
? [V4x0: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V5l )
& ( ( V3s @ V4x0 )
= ( V3s @ ( c_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) )
=> ( ? [V6i: tyop_2Enum_2Enum > A_27a,V7q: tyop_2Enum_2Enum > A_27state] :
( ( V1InitState @ ( V7q @ c_2Enum_2E0 ) )
& ! [V8t: tyop_2Enum_2Enum] : ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V6i @ V8t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V7q @ V8t ) @ ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V9t1: tyop_2Enum_2Enum] :
? [V10t2: tyop_2Enum_2Enum] : ( V2Accept @ ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) )
<=> ? [V11x0: tyop_2Enum_2Enum,V12l: tyop_2Enum_2Enum,V13j: tyop_2Enum_2Enum > A_27a,V14p: tyop_2Enum_2Enum > A_27state] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V12l )
& ! [V15t2: tyop_2Enum_2Enum] :
( ( V13j @ ( c_2Earithmetic_2E_2B @ V11x0 @ V15t2 ) )
= ( V13j @ ( c_2Earithmetic_2E_2B @ V11x0 @ ( c_2Earithmetic_2EMOD @ V15t2 @ V12l ) ) ) )
& ! [V16t2: tyop_2Enum_2Enum] :
( ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ V16t2 ) )
= ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ ( c_2Earithmetic_2EMOD @ V16t2 @ V12l ) ) ) )
& ( V1InitState @ ( V14p @ c_2Enum_2E0 ) )
& ! [V17t: tyop_2Enum_2Enum] : ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V13j @ V17t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V14p @ V17t ) @ ( V14p @ ( c_2Earithmetic_2E_2B @ V17t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V18t1: tyop_2Enum_2Enum] :
? [V19t2: tyop_2Enum_2Enum] : ( V2Accept @ ( V14p @ ( c_2Earithmetic_2E_2B @ V18t1 @ V19t2 ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PERIODIC__REDUCTION__THM,axiom,
! [A_27a: $tType,A_27state: $tType,V0TransRel: ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) > $o,V1InitState: A_27state > $o,V2Accept: A_27state > $o] :
( ! [V3s: tyop_2Enum_2Enum > A_27state] :
? [V4x0: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V5l )
& ( ( V3s @ V4x0 )
= ( V3s @ ( c_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) )
=> ( ? [V6i: tyop_2Enum_2Enum > A_27a,V7q: tyop_2Enum_2Enum > A_27state] :
( ( V1InitState @ ( V7q @ c_2Enum_2E0 ) )
& ! [V8t: tyop_2Enum_2Enum] : ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V6i @ V8t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V7q @ V8t ) @ ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V9t1: tyop_2Enum_2Enum] :
? [V10t2: tyop_2Enum_2Enum] : ( V2Accept @ ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) )
<=> ? [V11x0: tyop_2Enum_2Enum,V12l: tyop_2Enum_2Enum,V13j: tyop_2Enum_2Enum > A_27a,V14p: tyop_2Enum_2Enum > A_27state] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V12l )
& ! [V15t2: tyop_2Enum_2Enum] :
( ( V13j @ ( c_2Earithmetic_2E_2B @ V11x0 @ V15t2 ) )
= ( V13j @ ( c_2Earithmetic_2E_2B @ V11x0 @ ( c_2Earithmetic_2EMOD @ V15t2 @ V12l ) ) ) )
& ! [V16t2: tyop_2Enum_2Enum] :
( ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ V16t2 ) )
= ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ ( c_2Earithmetic_2EMOD @ V16t2 @ V12l ) ) ) )
& ( V1InitState @ ( V14p @ c_2Enum_2E0 ) )
& ! [V17t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V17t @ ( c_2Earithmetic_2E_2B @ V11x0 @ V12l ) )
=> ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V13j @ V17t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V14p @ V17t ) @ ( V14p @ ( c_2Earithmetic_2E_2B @ V17t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ? [V18t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V18t @ V12l )
& ( V2Accept @ ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ V18t ) ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EBUECHI__PROP__REDUCTION,axiom,
! [A_27a: $tType,A_27state: $tType,V0TransRel: ( tyop_2Epair_2Eprod @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) ) > $o,V1InitState: A_27state > $o,V2Accept: A_27state > $o] :
( ! [V3s: tyop_2Enum_2Enum > A_27state] :
? [V4x0: tyop_2Enum_2Enum,V5l: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V5l )
& ( ( V3s @ V4x0 )
= ( V3s @ ( c_2Earithmetic_2E_2B @ V4x0 @ V5l ) ) ) )
=> ( ? [V6i: tyop_2Enum_2Enum > A_27a,V7q: tyop_2Enum_2Enum > A_27state] :
( ( V1InitState @ ( V7q @ c_2Enum_2E0 ) )
& ! [V8t: tyop_2Enum_2Enum] : ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V6i @ V8t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V7q @ V8t ) @ ( V7q @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
& ! [V9t1: tyop_2Enum_2Enum] :
? [V10t2: tyop_2Enum_2Enum] : ( V2Accept @ ( V7q @ ( c_2Earithmetic_2E_2B @ V9t1 @ V10t2 ) ) ) )
<=> ? [V11x0: tyop_2Enum_2Enum,V12l: tyop_2Enum_2Enum,V13j: tyop_2Enum_2Enum > A_27a,V14p: tyop_2Enum_2Enum > A_27state] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ V12l )
& ( V1InitState @ ( V14p @ c_2Enum_2E0 ) )
& ! [V15t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V15t @ ( c_2Earithmetic_2E_2B @ V11x0 @ V12l ) )
=> ( V0TransRel @ ( c_2Epair_2E_2C @ A_27a @ ( tyop_2Epair_2Eprod @ A_27state @ A_27state ) @ ( V13j @ V15t ) @ ( c_2Epair_2E_2C @ A_27state @ A_27state @ ( V14p @ V15t ) @ ( V14p @ ( c_2Earithmetic_2E_2B @ V15t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
& ? [V16t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V16t @ V12l )
& ( V2Accept @ ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ V16t ) ) ) )
& ( ( V14p @ V11x0 )
= ( V14p @ ( c_2Earithmetic_2E_2B @ V11x0 @ V12l ) ) ) ) ) ) ).
thf(thm_2EOmega__Automata_2EEQUALITY__THM,axiom,
! [A_27a: $tType,V0x: A_27a,V1y: A_27a] :
( ( V0x = V1y )
<=> ! [V2P: A_27a > $o] :
( ( V2P @ V0x )
= ( V2P @ V1y ) ) ) ).
thf(thm_2EOmega__Automata_2ELESS__THM,axiom,
! [V0x: tyop_2Enum_2Enum,V1y: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0x @ V1y )
<=> ? [V2P: tyop_2Enum_2Enum > $o] :
( ( V2P @ V0x )
& ( (~) @ ( V2P @ V1y ) )
& ! [V3z: tyop_2Enum_2Enum] :
( ( V2P @ ( c_2Enum_2ESUC @ V3z ) )
=> ( V2P @ V3z ) ) ) ) ).
thf(thm_2EOmega__Automata_2EFORALL__EXISTS__THM,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ! [V1t1: tyop_2Enum_2Enum] :
? [V2t2: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V1t1 @ V2t2 ) )
<=> ! [V3t1: tyop_2Enum_2Enum] :
? [V4t2: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3t1 @ V4t2 )
& ( V0P @ V4t2 ) ) ) ).
thf(thm_2EOmega__Automata_2EEXISTS__FORALL__THM,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ? [V1t1: tyop_2Enum_2Enum] :
! [V2t2: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V1t1 @ V2t2 ) )
<=> ? [V3t1: tyop_2Enum_2Enum] :
! [V4t2: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3t1 @ V4t2 )
=> ( V0P @ V4t2 ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT__LEMMA,axiom,
! [A_27a: $tType,V0PHI: ( A_27a > $o ) > A_27a > $o] :
( ? [V1x: A_27a] :
! [V2p: A_27a > $o] : ( V0PHI @ V2p @ V1x )
<=> ? [V3q: A_27a > $o] :
( ! [V4x: A_27a] :
( ( V3q @ V4x )
=> ! [V5p: A_27a > $o] : ( V0PHI @ V5p @ V4x ) )
& ? [V6z: A_27a] : ( V3q @ V6z ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT1__THM,axiom,
! [A_27a: $tType,V0PHI: ( A_27a > $o ) > A_27a > $o] :
( ? [V1x: A_27a] :
! [V2p: A_27a > $o] : ( V0PHI @ V2p @ V1x )
<=> ? [V3q: A_27a > $o] :
! [V4p: A_27a > $o,V5x: A_27a] :
? [V6z: A_27a] :
( ( ( V3q @ V5x )
=> ( V0PHI @ V4p @ V5x ) )
& ( V3q @ V6z ) ) ) ).
thf(thm_2EOmega__Automata_2EELGOT2__THM,axiom,
! [A_27a: $tType,V0PHI: ( A_27a > $o ) > A_27a > $o] :
( ! [V1x: A_27a] :
? [V2p: A_27a > $o] : ( V0PHI @ V2p @ V1x )
<=> ! [V3q: A_27a > $o] :
? [V4p: A_27a > $o,V5x: A_27a] :
! [V6z: A_27a] :
( ( V3q @ V6z )
=> ( ( V0PHI @ V4p @ V5x )
& ( V3q @ V5x ) ) ) ) ).
%------------------------------------------------------------------------------