let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being really-closed Program of SCM+FSA
for a being Int-Location
for k being Element of NAT st I is_halting_on Initialized s,P & not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let s be State of SCM+FSA; :: thesis: for I being really-closed Program of SCM+FSA
for a being Int-Location
for k being Element of NAT st I is_halting_on Initialized s,P & not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let I be really-closed Program of SCM+FSA; :: thesis: for a being Int-Location
for k being Element of NAT st I is_halting_on Initialized s,P & not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let a be Int-Location; :: thesis: for k being Element of NAT st I is_halting_on Initialized s,P & not I destroys a holds
(IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
let k be Element of NAT ; :: thesis: ( I is_halting_on Initialized s,P & not I destroys a implies (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a )
set s0 = Initialized s;
set s1 = Initialize (Initialized s);
set P1 = P +* I;
assume I is_halting_on Initialized s,P ; :: thesis: ( I destroys a or (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a )
then A1: P +* I halts_on Initialize (Initialized s) ;
assume A2: not I destroys a ; :: thesis: (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),k)) . a
thus (IExec (I,P,s)) . a = (Result ((P +* I),(Initialize (Initialized s)))) . a by MEMSTR_0:44
.= (Result ((P +* I),(Initialize (Initialized s)))) . a
.= (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a by A1, EXTPRO_1:23
.= (Initialized s) . a by A2, SCMFSA7B:21
.= (Comput ((P +* I),(Initialize (Initialized s)),k)) . a by A2, SCMFSA7B:21 ; :: thesis: verum