let s be State of SCM+FSA ; :: thesis: for I being parahalting good 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),s) = DataPart s
set D = Int-Locations \/ FinSeq-Locations ;
let I be parahalting good 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),s) = DataPart s
let a be read-write Int-Location ; :: thesis: ( s . (intloc 0 ) = 1 & s . a <= 0 implies DataPart (IExec (Times a,I),s) = DataPart s )
assume A1: s . (intloc 0 ) = 1 ; :: thesis: ( not s . a <= 0 or DataPart (IExec (Times a,I),s) = DataPart s )
set s0 = Initialized s;
A2: Stop SCM+FSA is_halting_on Initialized s by SCMFSA7B:25;
assume s . a <= 0 ; :: thesis: DataPart (IExec (Times a,I),s) = DataPart s
then A3: (Initialized s) . a <= 0 by SCMFSA6C:3;
A4: IExec ((Stop SCM+FSA ) ';' (Stop SCM+FSA )),(Initialized s) = (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialized s))) +* (Start-At ((IC (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialized s)))) + (card (Stop SCM+FSA ))),SCM+FSA ) by SCMFSA6B:44;
A5: for f being FinSeq-Location holds (Initialized s) . f = s . f by SCMFSA6C:3;
A6: for a being read-write Int-Location holds (Initialized s) . a = s . a by SCMFSA6C:3;
A7: (Initialized s) . (intloc 0 ) = 1 by SCMFSA6C:3;
A8: Stop SCM+FSA is_closed_on Initialized s by SCMFSA7B:24;
then A9: Times a,I is_halting_on Initialized s by A3, A2, SCMFSA8B:24;
A10: Stop SCM+FSA is_halting_on Initialized s by SCMFSA7B:25;
A11: Stop SCM+FSA is_closed_on Initialized s by SCMFSA7B:24;
A12: DataPart (IExec (Stop SCM+FSA ),(Initialized s)) = DataPart ((Initialized (Initialized s)) +* (Start-At 0 ,SCM+FSA )) by Th38
.= DataPart ((Initialized s) +* (Start-At 0 ,SCM+FSA )) by Th15
.= DataPart (Initialized s) by SCMFSA8A:10 ;
Times a,I is_closed_on Initialized s by A3, A8, A2, SCMFSA8B:24;
then DataPart (IExec (Times a,I),s) = DataPart (IExec (Times a,I),(Initialized s)) by A9, A7, A6, A5, Th45
.= DataPart (IExec ((Stop SCM+FSA ) ';' (Stop SCM+FSA )),(Initialized s)) by A3, A11, A10, A7, Th73, SCMFSA8A:37 ;
hence DataPart (IExec (Times a,I),s) = DataPart (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialized s))) by A4, SCMFSA8A:10
.= DataPart (IExec (Stop SCM+FSA ),(Initialized s)) by A8, A2, A7, A12, Th46
.= DataPart s by A1, A12, Th27 ;
:: thesis: verum