let P be Instruction-Sequence of SCM+FSA; :: thesis: for s being State of SCM+FSA
for I being good parahalting Program of SCM+FSA
for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),P,s)) = DataPart s
let s be State of SCM+FSA; :: thesis: for I being good parahalting Program of SCM+FSA
for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),P,s)) = DataPart s
set D = Data-Locations ;
let I be good parahalting Program of SCM+FSA; :: thesis: for a being read-write Int-Location st s . (intloc 0) = 1 & s . a <= 0 holds
DataPart (IExec ((Times (a,I)),P,s)) = DataPart s
let a be read-write Int-Location; :: thesis: ( s . (intloc 0) = 1 & s . a <= 0 implies DataPart (IExec ((Times (a,I)),P,s)) = DataPart s )
assume A1: s . (intloc 0) = 1 ; :: thesis: ( not s . a <= 0 or DataPart (IExec ((Times (a,I)),P,s)) = DataPart s )
set s0 = Initialized s;
A2: Stop SCM+FSA is_halting_on Initialized s,P by SCMFSA7B:19;
assume s . a <= 0 ; :: thesis: DataPart (IExec ((Times (a,I)),P,s)) = DataPart s
then A3: (Initialized s) . a <= 0 by SCMFSA_M:37;
A4: IExec (((Stop SCM+FSA) ";" (Stop SCM+FSA)),P,(Initialized s)) = IncIC ((IExec ((Stop SCM+FSA),P,(IExec ((Stop SCM+FSA),P,(Initialized s))))),(card (Stop SCM+FSA))) by SCMFSA6B:20;
A5: (Initialized s) . (intloc 0) = 1 by SCMFSA_M:9;
A6: Stop SCM+FSA is_closed_on Initialized s,P by SCMFSA7B:18;
A7: Stop SCM+FSA is_halting_on Initialized s,P by SCMFSA7B:19;
A8: DataPart (IExec ((Stop SCM+FSA),P,(Initialized s))) = DataPart (Initialized (Initialized s)) by Th14
.= DataPart (Initialized s) ;
for I being Program of SCM+FSA st I is_closed_on Initialized s,P & I is_halting_on Initialized s,P holds
Directed I is_pseudo-closed_on Initialized s,P by SCMFSA8A:23;
then A9: Directed (Stop SCM+FSA) is_pseudo-closed_on Initialized s,P by A6, A7;
DataPart (IExec ((Times (a,I)),P,s)) = DataPart (IExec ((Times (a,I)),P,(Initialized s)))
.= DataPart (IExec (((Stop SCM+FSA) ";" (Stop SCM+FSA)),P,(Initialized s))) by A3, A5, Th44, A9 ;
hence DataPart (IExec ((Times (a,I)),P,s)) = DataPart (IExec ((Stop SCM+FSA),P,(IExec ((Stop SCM+FSA),P,(Initialized s))))) by A4, MEMSTR_0:79
.= DataPart (IExec ((Stop SCM+FSA),P,(Initialized s))) by A6, A2, A5, A8, Th20
.= DataPart s by A1, A8, SCMFSA_M:19 ;
:: thesis: verum