ITP001 Axioms: ITP044^5.ax
%------------------------------------------------------------------------------
% File : ITP044^5 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 set theory export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau20] Gauthier (2020), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : Temporal_Logic^2.ax [Gau20]
% : HL4044^5.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 176 ( 0 unt; 11 typ; 0 def)
% Number of atoms : 5119 ( 132 equ; 0 cnn)
% Maximal formula atoms : 115 ( 29 avg)
% Number of connectives : 7021 ( 55 ~; 27 |; 160 &;6345 @)
% ( 88 <=>; 346 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 12 avg;6345 nst)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 41 usr; 43 con; 0-2 aty)
% Number of variables : 655 ( 191 ^ 423 !; 41 ?; 655 :)
% SPC : TH0_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
thf(tp_c_2ETemporal__Logic_2EALWAYS,type,
c_2ETemporal__Logic_2EALWAYS: $i ).
thf(mem_c_2ETemporal__Logic_2EALWAYS,axiom,
mem @ c_2ETemporal__Logic_2EALWAYS @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2ETemporal__Logic_2EBEFORE,type,
c_2ETemporal__Logic_2EBEFORE: $i ).
thf(mem_c_2ETemporal__Logic_2EBEFORE,axiom,
mem @ c_2ETemporal__Logic_2EBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2EEVENTUAL,type,
c_2ETemporal__Logic_2EEVENTUAL: $i ).
thf(mem_c_2ETemporal__Logic_2EEVENTUAL,axiom,
mem @ c_2ETemporal__Logic_2EEVENTUAL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2ETemporal__Logic_2ENEXT,type,
c_2ETemporal__Logic_2ENEXT: $i ).
thf(mem_c_2ETemporal__Logic_2ENEXT,axiom,
mem @ c_2ETemporal__Logic_2ENEXT @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ).
thf(tp_c_2ETemporal__Logic_2ESBEFORE,type,
c_2ETemporal__Logic_2ESBEFORE: $i ).
thf(mem_c_2ETemporal__Logic_2ESBEFORE,axiom,
mem @ c_2ETemporal__Logic_2ESBEFORE @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2ESUNTIL,type,
c_2ETemporal__Logic_2ESUNTIL: $i ).
thf(mem_c_2ETemporal__Logic_2ESUNTIL,axiom,
mem @ c_2ETemporal__Logic_2ESUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2ESWHEN,type,
c_2ETemporal__Logic_2ESWHEN: $i ).
thf(mem_c_2ETemporal__Logic_2ESWHEN,axiom,
mem @ c_2ETemporal__Logic_2ESWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2EUNTIL,type,
c_2ETemporal__Logic_2EUNTIL: $i ).
thf(mem_c_2ETemporal__Logic_2EUNTIL,axiom,
mem @ c_2ETemporal__Logic_2EUNTIL @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2EUPTO,type,
c_2ETemporal__Logic_2EUPTO: $i ).
thf(mem_c_2ETemporal__Logic_2EUPTO,axiom,
mem @ c_2ETemporal__Logic_2EUPTO @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ bool ) ).
thf(tp_c_2ETemporal__Logic_2EWATCH,type,
c_2ETemporal__Logic_2EWATCH: $i ).
thf(mem_c_2ETemporal__Logic_2EWATCH,axiom,
mem @ c_2ETemporal__Logic_2EWATCH @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(tp_c_2ETemporal__Logic_2EWHEN,type,
c_2ETemporal__Logic_2EWHEN: $i ).
thf(mem_c_2ETemporal__Logic_2EWHEN,axiom,
mem @ c_2ETemporal__Logic_2EWHEN @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ( arr @ ty_2Enum_2Enum @ bool ) @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2ENEXT,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ V0P )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : ( ap @ V0P @ ( ap @ c_2Enum_2ESUC @ V1t ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EALWAYS,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EEVENTUAL,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EWATCH,axiom,
! [V0q: $i] :
( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V0q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> $false )
& ( ( p @ ( ap @ V0q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
<=> ( ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EUPTO,axiom,
! [V0t0: tp__ty_2Enum_2Enum,V1t1: tp__ty_2Enum_2Enum,V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ c_2ETemporal__Logic_2EUPTO @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) @ V2a ) ) ) )
<=> ! [V3t2: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V0t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) @ ( inj__ty_2Enum_2Enum @ V1t1 ) ) ) )
=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V3t2 ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2EBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ! [V5t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2ESWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2ESUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(ax_thm_2ETemporal__Logic_2ESBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWATCH__EXISTS,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
? [V2q: $i] :
( ( mem @ V2q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V2q ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWELL__ORDER,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ? [V1n: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1n ) ) )
<=> ? [V2m: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
& ! [V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) )
=> ~ ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWELL__ORDER__UNIQUE,axiom,
! [V0m2: tp__ty_2Enum_2Enum,V1m1: tp__ty_2Enum_2Enum,V2P: $i] :
( ( mem @ V2P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) )
& ! [V3n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ ( inj__ty_2Enum_2Enum @ V1m1 ) ) )
=> ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) )
& ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V0m2 ) ) )
& ! [V4n: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4n ) ) @ ( inj__ty_2Enum_2Enum @ V0m2 ) ) )
=> ~ ( p @ ( ap @ V2P @ ( inj__ty_2Enum_2Enum @ V4n ) ) ) ) )
=> ( V1m1 = V0m2 ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EDELTA__CASES,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ? [V2d: tp__ty_2Enum_2Enum] :
( ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2d ) ) )
=> ~ ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2d ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ! [V4d: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4d ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ( ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ! [V5t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ( ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ? [V5t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__IMP,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ? [V4t: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V2t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWATCH__SIGNAL,axiom,
! [V0q: $i] :
( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ( ! [V3t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ! [V4t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ! [V6t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
=> ( ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
=> ~ ( p @ ( ap @ V0q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ! [V8t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0q @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3delta: tp__ty_2Enum_2Enum] :
( ( ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ( ! [V3t: tp__ty_2Enum_2Enum] :
~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ! [V4t: tp__ty_2Enum_2Enum] : ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( ! [V6t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V5d ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3delta: tp__ty_2Enum_2Enum] :
( ( ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ? [V5t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
=> ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__SIGNAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3delta: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3delta ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V3delta ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENEXT__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
& ! [V3t3: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t3 ) ) )
=> ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) @ ( inj__ty_2Enum_2Enum @ V3t3 ) ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t1 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ c_2ETemporal__Logic_2EUPTO @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) @ V0a ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3t1: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p
@ ( ap @ c_2ETemporal__Logic_2EUPTO
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) )
=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p
@ ( ap @ c_2ETemporal__Logic_2EUPTO
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3t1: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p
@ ( ap @ c_2ETemporal__Logic_2EUPTO
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V4t ) ) ) ) ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3t1: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p
@ ( ap @ c_2ETemporal__Logic_2EUPTO
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__LINORD,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ! [V3t1: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) )
& ( p
@ ( ap @ c_2ETemporal__Logic_2EUPTO
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) )
@ ( ap @ ( ap @ ( c_2Epair_2E_2C @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ) @ ( inj__ty_2Enum_2Enum @ V3t1 ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) ) ) ) )
=> ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V3t1 ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0a )
@ V1t ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__NOT__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ~ ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
@ V2t0 ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__WHEN__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ V0a )
@ V2t ) )
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
@ V0a )
@ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__HW,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3q: $i] :
( ( mem @ V3q @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V3q ) @ V0a ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3q @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
| ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2EF ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ V1t ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
@ V2t ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__BEFORE,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2EF ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__BEFORE,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
@ V1t0 ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t0 ) ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ V2t0 ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__SWHEN__LEMMA,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( p
@ ( ap
@ ( ap
@ ( ap @ ( c_2Ebool_2ECOND @ bool )
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t1: $i] :
( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t2: $i] : ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t2 ) @ V2t1 ) ) ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t0: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V0b ) @ V4t0 ) ) @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V0b ) @ V4t0 ) ) ) ) )
@ ( ap @ ( c_2Ebool_2E_3F @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t1: $i] :
( ap @ ( c_2Ebool_2E_21 @ ty_2Enum_2Enum )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t2: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6t2 ) @ V5t1 ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V0b ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V6t2 ) @ V5t1 ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1t ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2ET ) )
@ V0a ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ V2t ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__NOT__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ~ ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
@ V2t0 ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V5t ) ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V5t ) ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__NOT__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2ET ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1t ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2ET ) )
@ V0a ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ V1b @ V4t ) ) ) )
@ V2t ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V5t ) ) ) )
@ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ V2t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ V1b @ V3t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__AS__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__AS__SBEFORE,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V1t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
@ V1t0 ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__AS__SBEFORE,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : c_2Ebool_2EF ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__AS__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_5C_2F
@ ( ap
@ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) @ ( ap @ V1b @ V3t ) ) ) )
@ V2t0 ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__AS__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__AS__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1b )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) @ ( ap @ V1b @ V2t ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__AS__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap
@ ( ap @ c_2Ebool_2E_2F_5C
@ ( ap @ c_2Ebool_2E_7E
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ V2t0 ) ) )
@ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1b ) @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__AS__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t0: $i] :
( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ V2t0 ) )
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) )
@ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : c_2Ebool_2ET ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ V0b @ V3t ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V1a )
= ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V10t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V1a @ V10t ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : ( ap @ V1a @ V8t ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V1a ) @ V1a )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ V0b @ V3t ) ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : c_2Ebool_2EF ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2ET ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : ( ap @ V1a @ V9t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__SIMP,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : c_2Ebool_2EF ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) )
& ( ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : c_2Ebool_2ET ) )
@ V0b )
= ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V5t ) ) ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : c_2Ebool_2EF ) )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a )
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : c_2Ebool_2ET ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V8t: $i] : c_2Ebool_2EF ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V1a )
= ( lam @ ty_2Enum_2Enum
@ ^ [V9t: $i] : c_2Ebool_2EF ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V2t ) ) ) ) )
@ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EIMMEDIATE__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V0b @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
=> ( ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ V2a @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ! [V3a: $i] :
( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V4a: $i] :
( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) )
& ! [V5a: $i] :
( ( mem @ V5a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V5a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ V5a @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ! [V6a: $i] :
( ( mem @ V6a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V6a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V7a: $i] :
( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V7a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENO__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V2t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
=> ( ! [V3a: $i] :
( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V4a: $i] :
( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V4a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ! [V5a: $i] :
( ( mem @ V5a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V5a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $true ) )
& ! [V6a: $i] :
( ( mem @ V6a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V6a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) )
& ! [V7a: $i] :
( ( mem @ V7a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V7a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> $false ) )
& ! [V8a: $i] :
( ( mem @ V8a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V8a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V8a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESOME__EVENT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V3a: $i] :
( ( mem @ V3a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V3a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) )
& ( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ! [V4a: $i] :
( ( mem @ V4a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V4a ) @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EMORE__EVENT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V2t ) ) @ ( ap @ V1b @ V2t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V3t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V4t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V4t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V4t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V5t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V5t ) ) @ ( ap @ V1b @ V5t ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V6t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V6t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V6t ) ) ) ) )
@ V1b ) )
& ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V7t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V0a @ V7t ) ) @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V7t ) ) ) ) )
@ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__NEXT,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V1t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0P @ V1t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0P ) @ V2t ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EAND__NEXT,axiom,
! [V0Q: $i] :
( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EOR__NEXT,axiom,
! [V0Q: $i] :
( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EIMP__NEXT,axiom,
! [V0Q: $i] :
( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEQUIV__NEXT,axiom,
! [V0Q: $i] :
( ( mem @ V0Q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1P: $i] :
( ( mem @ V1P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ V1P @ V2t ) ) @ ( ap @ V0Q @ V2t ) ) ) )
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ ( c_2Emin_2E_3D @ bool ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1P ) @ V3t ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0Q ) @ V3t ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__NEXT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V0a ) ) @ ( ap @ c_2ETemporal__Logic_2ENEXT @ V1b ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__REC,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0P ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__REC,axiom,
! [V0P: $i] :
( ( mem @ V0P @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( ( p @ ( ap @ V0P @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
| ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0P ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWATCH__REC,axiom,
! [V0q: $i] :
( ( mem @ V0q @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ~ ( p @ ( ap @ V0q @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0q ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWATCH @ V0q ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
| ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p @ ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
=> ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__REC,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ~ ( p @ ( ap @ V1b @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ( ( p @ ( ap @ V0a @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
| ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2ENEXT @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__FIX,axiom,
! [V0y: $i] :
( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V1a @ V2t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
<=> ( ( V0y
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ V1a ) )
| ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2EF ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__FIX,axiom,
! [V0y: $i] :
( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V2t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V2t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
<=> ( ( V0y
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V1a ) )
| ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : c_2Ebool_2ET ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__FIX,axiom,
! [V0y: $i] :
( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ ( ap @ ( c_2Ebool_2ECOND @ bool ) @ ( ap @ V1b @ V3t ) ) @ ( ap @ V2a @ V3t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) )
<=> ( ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V2a ) @ V1b ) )
| ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V2a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__FIX,axiom,
! [V0y: $i] :
( ( mem @ V0y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2a: $i] :
( ( mem @ V2a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( V0y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Emin_2E_3D_3D_3E @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V1b @ V3t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ V2a @ V3t ) ) @ ( ap @ V0y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
<=> ( ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V2a ) @ V1b ) )
| ( V0y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V2a ) @ V1b ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__FIX,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1a: $i] :
( ( mem @ V1a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2y: $i] :
( ( mem @ V2y @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( V2y
= ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ ( ap @ c_2Ebool_2E_2F_5C @ ( ap @ c_2Ebool_2E_7E @ ( ap @ V0b @ V3t ) ) ) @ ( ap @ ( ap @ c_2Ebool_2E_5C_2F @ ( ap @ V1a @ V3t ) ) @ ( ap @ V2y @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ V3t ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) )
<=> ( ( V2y
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V1a ) @ V0b ) )
| ( V2y
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V1a ) @ V0b ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3J: $i] :
( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3J: $i] :
( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ? [V3J: $i] :
( ( mem @ V3J @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V3J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2J: $i] :
( ( mem @ V2J @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V2J @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
& ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ( p @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) @ ( ap @ c_2Earithmetic_2ENUMERAL @ ( ap @ c_2Earithmetic_2EBIT1 @ ( inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__INVARIANT,axiom,
! [V0b: $i] :
( ( mem @ V0b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0b ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ? [V2J: $i] :
( ( mem @ V2J @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V2J @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) )
& ! [V3t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V3t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V2J @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ V2J @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
=> ( p @ ( ap @ V0b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ? [V3J1: $i] :
( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ? [V6J2: $i] :
( ( mem @ V6J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V8t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
=> ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ? [V3J1: $i] :
( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) )
& ? [V5J2: $i] :
( ( mem @ V5J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V5J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ! [V6t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V5J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V6t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V7t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V5J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ V5J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
=> ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__INVARIANT,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( ? [V3J1: $i] :
( ( mem @ V3J1 @ ( arr @ ty_2Enum_2Enum @ bool ) )
& ( p @ ( ap @ V3J1 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
& ! [V4t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ~ ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
=> ( p @ ( ap @ V3J1 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V4t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ! [V5d: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ V3J1 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
=> ~ ( p @ ( ap @ V1b @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V5d ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) )
& ? [V6J2: $i] :
( ( mem @ V6J2 @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) )
& ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) )
& ! [V7t: tp__ty_2Enum_2Enum] :
( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
| ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V7t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
& ! [V8t: tp__ty_2Enum_2Enum] :
( ( ( p @ ( ap @ ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) @ ( ap @ V6J2 @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
& ( ( surj__ty_2Enum_2Enum @ ( ap @ V6J2 @ ( ap @ c_2Enum_2ESUC @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) )
= fo__c_2Enum_2E0 ) )
=> ( p @ ( ap @ V0a @ ( ap @ ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V8t ) ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EALWAYS__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a )
= ( ap @ c_2ETemporal__Logic_2EALWAYS @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EEVENTUAL__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a )
= ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EWHEN__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EUNTIL__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2EBEFORE__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESWHEN__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESUNTIL__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ESBEFORE__IDEM,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ( ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b )
= ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) ) @ V1b ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__ALWAYS,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EALWAYS @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EEVENTUAL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__EVENTUAL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ c_2ETemporal__Logic_2EEVENTUAL @ V0a ) @ ( inj__ty_2Enum_2Enum @ V1t0 ) ) )
<=> ( p
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EALWAYS
@ ( lam @ ty_2Enum_2Enum
@ ^ [V2t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V2t ) ) ) )
@ ( inj__ty_2Enum_2Enum @ V1t0 ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__WHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__UNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__BEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2EBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2ESUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__SWHEN,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESWHEN @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EWHEN
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__SUNTIL,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESUNTIL @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EBEFORE
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
thf(conj_thm_2ETemporal__Logic_2ENOT__SBEFORE,axiom,
! [V0a: $i] :
( ( mem @ V0a @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V1b: $i] :
( ( mem @ V1b @ ( arr @ ty_2Enum_2Enum @ bool ) )
=> ! [V2t0: tp__ty_2Enum_2Enum] :
( ~ ( p @ ( ap @ ( ap @ ( ap @ c_2ETemporal__Logic_2ESBEFORE @ V0a ) @ V1b ) @ ( inj__ty_2Enum_2Enum @ V2t0 ) ) )
<=> ( p
@ ( ap
@ ( ap
@ ( ap @ c_2ETemporal__Logic_2EUNTIL
@ ( lam @ ty_2Enum_2Enum
@ ^ [V3t: $i] : ( ap @ c_2Ebool_2E_7E @ ( ap @ V0a @ V3t ) ) ) )
@ V1b )
@ ( inj__ty_2Enum_2Enum @ V2t0 ) ) ) ) ) ) ).
%------------------------------------------------------------------------------