ITP001 Axioms: ITP044^7.ax
%------------------------------------------------------------------------------
% File : ITP044^7 : 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 : Temporal_Logic.ax [Gau19]
% : HL4044^7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 195 ( 85 unt; 34 typ; 0 def)
% Number of atoms : 863 ( 151 equ; 56 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 2321 ( 56 ~; 28 |; 142 &;1964 @)
% ( 77 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg;1964 nst)
% Number of types : 3 ( 2 usr)
% Number of type conns : 405 ( 405 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 32 usr; 5 con; 0-4 aty)
% Number of variables : 677 ( 191 ^ 438 !; 42 ?; 677 :)
% ( 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_2Earithmetic_2E_3C_3D,type,
c_2Earithmetic_2E_3C_3D: 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_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_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_2EUPTO,type,
c_2ETemporal__Logic_2EUPTO: ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) ) > $o ).
thf(c_2ETemporal__Logic_2EWATCH,type,
c_2ETemporal__Logic_2EWATCH: ( 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_2ETemporal__Logic_2ENEXT,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ V0P )
= ( ^ [V1t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Enum_2ESUC @ V1t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS,axiom,
! [V0P: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0P @ V1t0 )
<=> ! [V2t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V2t @ V1t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL,axiom,
! [V0P: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0P @ V1t0 )
<=> ? [V2t: tyop_2Enum_2Enum] : ( V0P @ ( c_2Earithmetic_2E_2B @ V2t @ V1t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EWATCH,axiom,
! [V0q: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EWATCH @ V0q @ V1b @ V2t0 )
<=> ! [V3t: tyop_2Enum_2Enum] :
( ( ( V0q @ V2t0 )
= c_2Ebool_2EF )
& ( ( V0q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) ) )
<=> ( ( V0q @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V2t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUPTO,axiom,
! [V0t0: tyop_2Enum_2Enum,V1t1: tyop_2Enum_2Enum,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUPTO @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V1t1 @ V2a ) ) )
<=> ! [V3t2: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t2 )
& ( c_2Eprim__rec_2E_3C @ V3t2 @ V1t1 ) )
=> ( V2a @ V3t2 ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EWHEN @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
| ( ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
=> ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EUNTIL @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
| ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EBEFORE @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ( ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
| ! [V5t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V2t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2ESWHEN @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
& ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
| ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ? [V5t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V0a @ V1b @ V2t0 )
<=> ? [V3q: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V2t0 )
& ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) )
& ( V0a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWATCH__EXISTS,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1t0: tyop_2Enum_2Enum] :
? [V2q: tyop_2Enum_2Enum > $o] : ( c_2ETemporal__Logic_2EWATCH @ V2q @ V0b @ V1t0 ) ).
thf(thm_2ETemporal__Logic_2EWELL__ORDER,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ? [V1n: tyop_2Enum_2Enum] : ( V0P @ V1n )
<=> ? [V2m: tyop_2Enum_2Enum] :
( ( V0P @ V2m )
& ! [V3n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3n @ V2m )
=> ( (~) @ ( V0P @ V3n ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE,axiom,
! [V0m2: tyop_2Enum_2Enum,V1m1: tyop_2Enum_2Enum,V2P: tyop_2Enum_2Enum > $o] :
( ( ( V2P @ V1m1 )
& ! [V3n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3n @ V1m1 )
=> ( (~) @ ( V2P @ V3n ) ) )
& ( V2P @ V0m2 )
& ! [V4n: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4n @ V0m2 )
=> ( (~) @ ( V2P @ V4n ) ) ) )
=> ( V1m1 = V0m2 ) ) ).
thf(thm_2ETemporal__Logic_2EDELTA__CASES,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ? [V2d: tyop_2Enum_2Enum] :
( ! [V3t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V3t @ V2d )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V2d @ V0t0 ) ) )
| ! [V4d: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4d @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ( ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
| ! [V5t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ( ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ? [V5t: tyop_2Enum_2Enum] : ( V1b @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__IMP,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V1b @ V0t0 )
=> ? [V4t: tyop_2Enum_2Enum] :
( ( (~) @ ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
<=> ! [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 )
<=> ? [V2t: tyop_2Enum_2Enum] : ( V1a @ ( c_2Earithmetic_2E_2B @ V2t @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EWATCH__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1q: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b @ V0t0 )
<=> ( ( ! [V3t: tyop_2Enum_2Enum] : ( (~) @ ( V2b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
=> ! [V4t: tyop_2Enum_2Enum] : ( (~) @ ( V1q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( ( V2b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
& ! [V6t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V6t @ V5d )
=> ( (~) @ ( V2b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) ) )
=> ( ! [V7t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V7t @ V5d )
=> ( (~) @ ( V1q @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) )
& ! [V8t: tyop_2Enum_2Enum] : ( V1q @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ! [V3delta: tyop_2Enum_2Enum] :
( ( ! [V4t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
<=> ( ( ! [V3t: tyop_2Enum_2Enum] : ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
=> ! [V4t: tyop_2Enum_2Enum] : ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( ! [V6t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V6t @ V5d )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
=> ! [V7t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V7t @ V5d )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ! [V3delta: tyop_2Enum_2Enum] :
( ( ! [V4t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) )
=> ? [V5t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V5t @ V3delta )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V5t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ! [V4t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) )
& ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ! [V4t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V4t @ V3delta )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) )
& ( V1b @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__SIGNAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3delta: tyop_2Enum_2Enum] :
( ( V2a @ ( c_2Earithmetic_2E_2B @ V3delta @ V0t0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V4t @ V3delta )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ENEXT__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ V1a @ V0t0 )
<=> ? [V2t1: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0t0 @ V2t1 )
& ! [V3t3: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ V0t0 @ V3t3 )
=> ( c_2Earithmetic_2E_3C_3D @ V2t1 @ V3t3 ) )
& ( V1a @ V2t1 ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
<=> ! [V2t1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V2t1 )
=> ( V1a @ V2t1 ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 )
<=> ? [V2t1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V2t1 )
& ( V1a @ V2t1 ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ? [V3t1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( V1b @ V3t1 )
& ( c_2ETemporal__Logic_2EUPTO @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0 @ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1 @ V2a ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
<=> ! [V3t1: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( (~) @ ( V1b @ V3t1 ) )
& ( c_2ETemporal__Logic_2EUPTO
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) )
=> ( V2a @ V3t1 ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3t1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( V2a @ V3t1 )
& ( (~) @ ( V1b @ V3t1 ) )
& ( c_2ETemporal__Logic_2EUPTO
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ! [V3t1: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( c_2ETemporal__Logic_2EUPTO
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V4t ) ) ) ) ) )
=> ( (~) @ ( V1b @ V3t1 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3t1: tyop_2Enum_2Enum] :
( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( V2a @ V3t1 )
& ( V1b @ V3t1 )
& ( c_2ETemporal__Logic_2EUPTO
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__LINORD,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ! [V3t1: tyop_2Enum_2Enum] :
( ( ( c_2Earithmetic_2E_3C_3D @ V0t0 @ V3t1 )
& ( V1b @ V3t1 )
& ( c_2ETemporal__Logic_2EUPTO
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Epair_2Eprod @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) ) @ V0t0
@ ( c_2Epair_2E_2C @ tyop_2Enum_2Enum @ ( tyop_2Enum_2Enum > $o ) @ V3t1
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V4t ) ) ) ) ) )
=> ( V2a @ V3t1 ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__WHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( c_2ETemporal__Logic_2EWHEN
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__WHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( ^ [V1t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0a
@ V1t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__AS__WHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN @ V0b
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V2t ) @ ( V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__WHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__NOT__WHEN,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ( (~)
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__AS__WHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2ETemporal__Logic_2EWHEN @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
@ V2t )
@ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__AS__WHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
@ V2t0 )
@ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__WHEN__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ V1a
@ V2t )
@ ( c_2ETemporal__Logic_2EWHEN
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
@ V1a
@ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__HW,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] :
( ( c_2ETemporal__Logic_2EWATCH @ V3q @ V2a @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( V3q @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
| ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__UNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( c_2ETemporal__Logic_2EUNTIL @ V0a
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__UNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( ^ [V1t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
@ V2t )
@ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__AS__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__AS__UNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0b )
= ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0b )
= ( ^ [V1t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b
@ V1t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
@ V2t0 ) )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) )
@ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__AS__BEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b @ V2t0 ) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__SWHEN__LEMMA,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( c_2Ebool_2ECOND @ $o
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V2t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V3t2: tyop_2Enum_2Enum] : ( V0b @ ( c_2Earithmetic_2E_2B @ V3t2 @ V2t1 ) ) ) )
@ ( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V4t0: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ V4t0 ) @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ V4t0 ) ) )
@ ( c_2Ebool_2E_3F @ tyop_2Enum_2Enum
@ ^ [V5t1: tyop_2Enum_2Enum] :
( c_2Ebool_2E_21 @ tyop_2Enum_2Enum
@ ^ [V6t2: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b @ ( c_2Earithmetic_2E_2B @ V6t2 @ V5t1 ) ) @ ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ ( c_2Earithmetic_2E_2B @ V6t2 @ V5t1 ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__SWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( ^ [V1t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V3t ) )
@ V1t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SWHEN,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0a ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b @ V2t )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__NOT__SWHEN,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ( (~)
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__AS__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ESWHEN @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
@ V2t )
@ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
@ V2t0 )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V5t ) ) @ ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__NOT__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESWHEN @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__AS__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN @ V0b
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1a @ V2t ) @ ( V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__AS__SWHEN,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__SUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( ^ [V1t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0a @ V3t ) )
@ V1t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SUNTIL,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0a ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__SUNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( V0b @ V4t ) )
@ V2t )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) )
@ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__AS__SUNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b @ V2t ) @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__SUNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__SUNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( V0b @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__AS__SUNTIL,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) )
@ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0b )
= ( ^ [V1t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V2t ) )
@ ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V1t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V1t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F
@ ( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V3t ) ) @ ( V0b @ V3t ) )
@ V2t0 )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V4t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE @ V0b
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V1a @ V2t ) ) @ ( V0b @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_2F_5C
@ ( c_2Ebool_2E_7E
@ ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V3t ) )
@ V0b
@ V2t0 ) )
@ ( c_2ETemporal__Logic_2EEVENTUAL @ V0b @ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__AS__SBEFORE,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( ^ [V2t0: tyop_2Enum_2Enum] :
( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b @ V2t0 )
@ ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) )
@ V2t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a
@ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) )
& ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V1a )
= ( ^ [V10t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( V0b @ V3t ) ) )
& ( ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a
@ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V1a )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a
@ ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V1a )
= ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V10t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V10t ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
@ ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a
@ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V8t: tyop_2Enum_2Enum] : ( V1a @ V8t ) ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V1a )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( V0b @ V3t ) ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
@ ^ [V5t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a
@ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V1a )
= ( ^ [V9t: tyop_2Enum_2Enum] : ( V1a @ V9t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__SIMP,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : c_2Ebool_2EF
@ V0b )
= ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V4t: tyop_2Enum_2Enum] : c_2Ebool_2ET
@ V0b )
= ( ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0b @ V5t ) ) ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
@ ^ [V6t: tyop_2Enum_2Enum] : c_2Ebool_2EF )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a
@ ^ [V7t: tyop_2Enum_2Enum] : c_2Ebool_2ET )
= ( ^ [V8t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V1a )
= ( ^ [V9t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V2t ) ) )
@ V0b ) ) ).
thf(thm_2ETemporal__Logic_2EIMMEDIATE__EVENT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( V1b @ V0t0 )
=> ( ! [V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
= ( V2a @ V0t0 ) )
& ! [V3a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V3a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V4a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V4a @ V1b @ V0t0 )
= c_2Ebool_2EF )
& ! [V5a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V5a @ V1b @ V0t0 )
= ( V5a @ V0t0 ) )
& ! [V6a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V6a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V7a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V7a @ V1b @ V0t0 )
= c_2Ebool_2EF ) ) ) ).
thf(thm_2ETemporal__Logic_2ENO__EVENT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1b @ V2t ) )
@ V0t0 )
=> ( ! [V3a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V3a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V4a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V4a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2EALWAYS @ V4a @ V0t0 ) )
& ! [V5a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V5a @ V1b @ V0t0 )
= c_2Ebool_2ET )
& ! [V6a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V6a @ V1b @ V0t0 )
= c_2Ebool_2EF )
& ! [V7a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V7a @ V1b @ V0t0 )
= c_2Ebool_2EF )
& ! [V8a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V8a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2EEVENTUAL @ V8a @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESOME__EVENT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V3a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V3a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESUNTIL @ V3a @ V1b @ V0t0 ) ) )
& ( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ! [V4a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V4a @ V1b @ V0t0 )
= ( c_2ETemporal__Logic_2ESBEFORE @ V4a @ V1b @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EMORE__EVENT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0b @ V2t ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V3t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V4t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V4t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V4t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V5t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V5t ) @ ( V0b @ V5t ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V6t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V6t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V6t ) ) )
@ V0b ) )
& ( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V7t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V7t ) @ ( c_2Ebool_2E_7E @ ( V0b @ V7t ) ) )
@ V0b ) ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__NEXT,axiom,
! [V0P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V1t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V0P @ V1t ) ) )
= ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( c_2ETemporal__Logic_2ENEXT @ V0P @ V2t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EAND__NEXT,axiom,
! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EOR__NEXT,axiom,
! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EIMP__NEXT,axiom,
! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEQUIV__NEXT,axiom,
! [V0Q: tyop_2Enum_2Enum > $o,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( V1P @ V2t ) @ ( V0Q @ V2t ) ) )
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D @ $o @ ( c_2ETemporal__Logic_2ENEXT @ V1P @ V3t ) @ ( c_2ETemporal__Logic_2ENEXT @ V0Q @ V3t ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V0a ) )
= ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
= ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__NEXT,axiom,
! [V0a: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V0a @ V1b ) )
= ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V1P @ V0t0 )
<=> ( ( V1P @ V0t0 )
& ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1P ) @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1P: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V1P @ V0t0 )
<=> ( ( V1P @ V0t0 )
| ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1P ) @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EWATCH__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1q: tyop_2Enum_2Enum > $o,V2b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b @ V0t0 )
<=> ( ( (~) @ ( V1q @ V0t0 ) )
& ( c_2Ebool_2ECOND @ $o @ ( V2b @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EALWAYS @ V1q ) @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWATCH @ V1q @ V2b ) @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V0t0 ) @ ( V2a @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 )
<=> ( ( (~) @ ( V1b @ V0t0 ) )
=> ( ( V2a @ V0t0 )
& ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ( ( (~) @ ( V1b @ V0t0 ) )
& ( ( V2a @ V0t0 )
| ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b ) @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
= ( c_2Ebool_2ECOND @ $o @ ( V1b @ V0t0 ) @ ( V2a @ V0t0 ) @ ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) @ V0t0 ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ( ( (~) @ ( V1b @ V0t0 ) )
=> ( ( V2a @ V0t0 )
& ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__REC,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ( ( (~) @ ( V1b @ V0t0 ) )
& ( ( V2a @ V0t0 )
| ( c_2ETemporal__Logic_2ENEXT @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b ) @ V0t0 ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__FIX,axiom,
! [V0y: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( V0y
= ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( V1a @ V2t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V2t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EALWAYS @ V1a ) )
| ( V0y
= ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2EF ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__FIX,axiom,
! [V0y: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( V0y
= ( ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_5C_2F @ ( V1a @ V2t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V2t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
| ( V0y
= ( ^ [V3t: tyop_2Enum_2Enum] : c_2Ebool_2ET ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__FIX,axiom,
! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( V0y
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND @ $o @ ( V1b @ V3t ) @ ( V2a @ V3t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b ) )
| ( V0y
= ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__FIX,axiom,
! [V0y: tyop_2Enum_2Enum > $o,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( V0y
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Emin_2E_3D_3D_3E @ ( c_2Ebool_2E_7E @ ( V1b @ V3t ) ) @ ( c_2Ebool_2E_2F_5C @ ( V2a @ V3t ) @ ( V0y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
<=> ( ( V0y
= ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b ) )
| ( V0y
= ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__FIX,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o,V2y: tyop_2Enum_2Enum > $o] :
( ( V2y
= ( ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_2F_5C @ ( c_2Ebool_2E_7E @ ( V0b @ V3t ) ) @ ( c_2Ebool_2E_5C_2F @ ( V1a @ V3t ) @ ( V2y @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
<=> ( ( V2y
= ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) )
| ( V2y
= ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 )
<=> ? [V3J: tyop_2Enum_2Enum > $o] :
( ( V3J @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
=> ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
& ( V3J @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__INVARIANT,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o,V2t0: tyop_2Enum_2Enum] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b @ V2t0 )
<=> ? [V3J: tyop_2Enum_2Enum > $o] :
( ( V3J @ V2t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
& ( (~) @ ( V0b @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) )
=> ( ( V1a @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) )
& ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V2t0 ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 )
<=> ? [V3J: tyop_2Enum_2Enum > $o] :
( ( V3J @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( V3J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
=> ( V3J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( V3J @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 )
<=> ? [V2J: tyop_2Enum_2Enum > $o] :
( ( V2J @ V0t0 )
& ! [V3t: tyop_2Enum_2Enum] :
( ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) )
=> ( ( V1a @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) )
& ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ ( c_2Earithmetic_2E_2B @ V0t0 @ ( c_2Earithmetic_2ENUMERAL @ ( c_2Earithmetic_2EBIT1 @ c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V1b @ V0t0 )
<=> ? [V2J: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V2J @ V0t0 ) )
& ! [V3t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) ) @ ( V2J @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
| ( ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V3t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V2J @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( ( V2J @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
=> ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 )
<=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
( ( V3J1 @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
& ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) )
=> ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
& ( V3J1 @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) )
& ? [V6J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ V0t0 ) )
& ! [V7t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
| ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
& ! [V8t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
& ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
=> ( V1b @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 )
<=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
( ( V3J1 @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
=> ( ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) ) ) )
& ? [V5J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V5J2 @ V0t0 ) )
& ! [V6t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) ) @ ( V5J2 @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
| ( ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V6t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
& ! [V7t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V5J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
& ( ( V5J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
=> ( V1b @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__INVARIANT,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 )
<=> ( ? [V3J1: tyop_2Enum_2Enum > $o] :
( ( V3J1 @ V0t0 )
& ! [V4t: tyop_2Enum_2Enum] :
( ( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) )
& ( (~) @ ( V2a @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
=> ( V3J1 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V4t @ V0t0 ) ) ) )
& ! [V5d: tyop_2Enum_2Enum] :
( ( V3J1 @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) )
=> ( (~) @ ( V1b @ ( c_2Earithmetic_2E_2B @ V5d @ V0t0 ) ) ) ) )
& ? [V6J2: tyop_2Enum_2Enum > tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ V0t0 ) )
& ! [V7t: tyop_2Enum_2Enum] :
( ( c_2Eprim__rec_2E_3C @ ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) ) @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
| ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V7t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
& ! [V8t: tyop_2Enum_2Enum] :
( ( ( c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ ( V6J2 @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
& ( ( V6J2 @ ( c_2Enum_2ESUC @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) )
= c_2Enum_2E0 ) )
=> ( V2a @ ( c_2Earithmetic_2E_2B @ V8t @ V0t0 ) ) ) ) ) ) ).
thf(thm_2ETemporal__Logic_2EALWAYS__IDEM,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( c_2ETemporal__Logic_2EALWAYS @ ( c_2ETemporal__Logic_2EALWAYS @ V0a ) ) ) ).
thf(thm_2ETemporal__Logic_2EEVENTUAL__IDEM,axiom,
! [V0a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( c_2ETemporal__Logic_2EEVENTUAL @ ( c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) ) ).
thf(thm_2ETemporal__Logic_2EWHEN__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EWHEN @ ( c_2ETemporal__Logic_2EWHEN @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2EUNTIL__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EUNTIL @ ( c_2ETemporal__Logic_2EUNTIL @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2EBEFORE__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2EBEFORE @ ( c_2ETemporal__Logic_2EBEFORE @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESWHEN__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESWHEN @ ( c_2ETemporal__Logic_2ESWHEN @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESUNTIL__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESUNTIL @ ( c_2ETemporal__Logic_2ESUNTIL @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ESBEFORE__IDEM,axiom,
! [V0b: tyop_2Enum_2Enum > $o,V1a: tyop_2Enum_2Enum > $o] :
( ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b )
= ( c_2ETemporal__Logic_2ESBEFORE @ ( c_2ETemporal__Logic_2ESBEFORE @ V1a @ V0b ) @ V0b ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__ALWAYS,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2EALWAYS @ V1a @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2EEVENTUAL
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) )
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__EVENTUAL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2EEVENTUAL @ V1a @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2EALWAYS
@ ^ [V2t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V1a @ V2t ) )
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__WHEN,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2EWHEN @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2ESWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__UNTIL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2EUNTIL @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2ESBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__BEFORE,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2EBEFORE @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2ESUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__SWHEN,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2ESWHEN @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2EWHEN
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__SUNTIL,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2ESUNTIL @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2EBEFORE
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
thf(thm_2ETemporal__Logic_2ENOT__SBEFORE,axiom,
! [V0t0: tyop_2Enum_2Enum,V1b: tyop_2Enum_2Enum > $o,V2a: tyop_2Enum_2Enum > $o] :
( ( (~) @ ( c_2ETemporal__Logic_2ESBEFORE @ V2a @ V1b @ V0t0 ) )
<=> ( c_2ETemporal__Logic_2EUNTIL
@ ^ [V3t: tyop_2Enum_2Enum] : ( c_2Ebool_2E_7E @ ( V2a @ V3t ) )
@ V1b
@ V0t0 ) ) ).
%------------------------------------------------------------------------------