let s be State of SCM+FSA ; :: thesis: for I being good InitHalting 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
let I be good InitHalting 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 )
assume s . a <= 0 ; :: thesis: DataPart (IExec (Times a,I),s) = DataPart s
then A2: (Initialize s) . a <= 0 by SCMFSA6C:3;
set P = if=0 a,(Goto (insloc 2)),(I ';' (SubFrom a,(intloc 0 )));
set s0 = Initialize s;
A4: ( Stop SCM+FSA is_closed_on Initialize s & Stop SCM+FSA is_halting_on Initialize s ) by SCMFSA7B:24, SCMFSA7B:25;
then A5: ( Times a,I is_closed_on Initialize s & Times a,I is_halting_on Initialize s ) by A2, SCMFSA8B:24;
B6: ( Stop SCM+FSA is_closed_on Initialize s & Stop SCM+FSA is_halting_on Initialize s ) by SCMFSA7B:24, SCMFSA7B:25;
A7: ( (Initialize s) . (intloc 0 ) = 1 & ( for a being read-write Int-Location holds (Initialize s) . a = s . a ) & ( for f being FinSeq-Location holds (Initialize s) . f = s . f ) ) by SCMFSA6C:3;
then A8: DataPart (IExec (Times a,I),s) = DataPart (IExec (Times a,I),(Initialize s)) by A5, SCMFSA8C:45
.= DataPart (IExec ((Stop SCM+FSA ) ';' (Stop SCM+FSA )),(Initialize s)) by A2, B6, A7, SCMFSA8A:37, SCMFSA8C:73 ;
A9: DataPart (IExec (Stop SCM+FSA ),(Initialize s)) = DataPart ((Initialize (Initialize s)) +* (Start-At (insloc 0 ))) by SCMFSA8C:38
.= DataPart ((Initialize s) +* (Start-At (insloc 0 ))) by SCMFSA8C:15
.= DataPart (Initialize s) by SCMFSA8A:10 ;
IExec ((Stop SCM+FSA ) ';' (Stop SCM+FSA )),(Initialize s) = (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialize s))) +* (Start-At ((IC (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialize s)))) + (card (Stop SCM+FSA )))) by SCMFSA6B:44;
hence DataPart (IExec (Times a,I),s) = DataPart (IExec (Stop SCM+FSA ),(IExec (Stop SCM+FSA ),(Initialize s))) by A8, SCMFSA8A:10
.= DataPart (IExec (Stop SCM+FSA ),(Initialize s)) by A4, A7, A9, SCMFSA8C:46
.= DataPart s by A1, A9, SCMFSA8C:27 ;
:: thesis: verum