let s be State of SCM+FSA; :: thesis: for p being Instruction-Sequence of SCM+FSA
for f being FinSeq-Location
for I being Program of SCM+FSA st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not f in UsedInt*Loc I holds
(IExec (I,p,s)) . f = (Initialized s) . f
let p be Instruction-Sequence of SCM+FSA; :: thesis: for f being FinSeq-Location
for I being Program of SCM+FSA st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not f in UsedInt*Loc I holds
(IExec (I,p,s)) . f = (Initialized s) . f
let f be FinSeq-Location ; :: thesis: for I being Program of SCM+FSA st I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not f in UsedInt*Loc I holds
(IExec (I,p,s)) . f = (Initialized s) . f
let I be Program of SCM+FSA; :: thesis: ( I is_closed_on Initialized s,p & I is_halting_on Initialized s,p & not f in UsedInt*Loc I implies (IExec (I,p,s)) . f = (Initialized s) . f )
set a = f;
assume that
A1: I is_closed_on Initialized s,p and
A2: I is_halting_on Initialized s,p and
A3: not f in UsedInt*Loc I ; :: thesis: (IExec (I,p,s)) . f = (Initialized s) . f
set Is = Initialized s;
set pI = p +* I;
A6: p +* I halts_on Initialize (Initialized s) by A2, SCMFSA7B:def 7;
A9: Initialized s = Initialize (Initialized s) by MEMSTR_0:44;
for m being Element of NAT st m < LifeSpan ((p +* I),(Initialized s)) holds
IC (Comput ((p +* I),(Initialized s),m)) in dom I by A1, A9, SCMFSA7B:def 6;
then A10: (Comput ((p +* I),(Initialized s),(LifeSpan ((p +* I),(Initialized s))))) . f = (Initialized s) . f by A3, FUNCT_4:25, SF_MASTR:63;
DataPart (IExec (I,p,s)) = DataPart (Result ((p +* I),(Initialized s))) by SCMFSA6B:def 1
.= DataPart (Result ((p +* I),(Initialized s)))
.= DataPart (Comput ((p +* I),(Initialized s),(LifeSpan ((p +* I),(Initialized s))))) by A9, A6, EXTPRO_1:23 ;
hence (IExec (I,p,s)) . f = (Initialized s) . f by A10, SCMFSA6A:7; :: thesis: verum