let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA
for f being FinSeq-Location
for I being really-closed Program of st I is_halting_on Initialized s,p & not f in UsedI*Loc I holds
(IExec (I,p,s)) . f = () . f

let p be Instruction-Sequence of SCM+FSA; :: thesis: for f being FinSeq-Location
for I being really-closed Program of st I is_halting_on Initialized s,p & not f in UsedI*Loc I holds
(IExec (I,p,s)) . f = () . f

let f be FinSeq-Location ; :: thesis: for I being really-closed Program of st I is_halting_on Initialized s,p & not f in UsedI*Loc I holds
(IExec (I,p,s)) . f = () . f

let I be really-closed Program of ; :: thesis: ( I is_halting_on Initialized s,p & not f in UsedI*Loc I implies (IExec (I,p,s)) . f = () . f )
set a = f;
assume that
A1: I is_halting_on Initialized s,p and
A2: not f in UsedI*Loc I ; :: thesis: (IExec (I,p,s)) . f = () . f
set Is = Initialized s;
set pI = p +* I;
A3: p +* I halts_on Initialize () by ;
A4: Initialized s = Initialize () by MEMSTR_0:44;
A5: I c= p +* I by FUNCT_4:25;
IC () = 0 by MEMSTR_0:def 11;
then IC () in dom I by AFINSQ_1:65;
then for m being Nat st m < LifeSpan ((p +* I),()) holds
IC (Comput ((p +* I),(),m)) in dom I by ;
then A6: (Comput ((p +* I),(),(LifeSpan ((p +* I),())))) . f = () . f by ;
DataPart (IExec (I,p,s)) = DataPart (Result ((p +* I),())) by SCMFSA6B:def 1
.= DataPart (Result ((p +* I),()))
.= DataPart (Comput ((p +* I),(),(LifeSpan ((p +* I),())))) by ;
hence (IExec (I,p,s)) . f = () . f by ; :: thesis: verum