let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds
( ( for a being read-write Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a ) & ( for f being FinSeq-Location holds (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f ) )
let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA st I is_halting_on Initialized s,P holds
( ( for a being read-write Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a ) & ( for f being FinSeq-Location holds (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f ) )
let I be Program of SCM+FSA; :: thesis: ( I is_halting_on Initialized s,P implies ( ( for a being read-write Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a ) & ( for f being FinSeq-Location holds (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f ) ) )
set s0 = Initialized s;
set s1 = Initialize (Initialized s);
set P1 = P +* I;
assume I is_halting_on Initialized s,P ; :: thesis: ( ( for a being read-write Int-Location holds (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . a ) & ( for f being FinSeq-Location holds (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f ) )
then A1: P +* I halts_on Initialize (Initialized s) ;
hereby :: thesis: for f being FinSeq-Location holds (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f
let a be read-write Int-Location; :: thesis: (IExec (I,P,s)) . a = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . 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 ; :: thesis: verum
end;
let f be FinSeq-Location ; :: thesis: (IExec (I,P,s)) . f = (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f
thus (IExec (I,P,s)) . f = (Result ((P +* I),(Initialize (Initialized s)))) . f by MEMSTR_0:44
.= (Result ((P +* I),(Initialize (Initialized s)))) . f
.= (Comput ((P +* I),(Initialize (Initialized s)),(LifeSpan ((P +* I),(Initialize (Initialized s)))))) . f by A1, EXTPRO_1:23 ; :: thesis: verum