let s be State of SCM+FSA; :: thesis: for P being Instruction-Sequence of SCM+FSA
for I being Program of SCM+FSA st I is_closed_on Initialized s,P & I is_halting_on Initialized s,P holds
IExec ((I ';' (Stop SCM+FSA)),P,s) = (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA))
let P be Instruction-Sequence of SCM+FSA; :: thesis: for I being Program of SCM+FSA st I is_closed_on Initialized s,P & I is_halting_on Initialized s,P holds
IExec ((I ';' (Stop SCM+FSA)),P,s) = (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA))
let I be Program of SCM+FSA; :: thesis: ( I is_closed_on Initialized s,P & I is_halting_on Initialized s,P implies IExec ((I ';' (Stop SCM+FSA)),P,s) = (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA)) )
assume A1: I is_closed_on Initialized s,P ; :: thesis: ( not I is_halting_on Initialized s,P or IExec ((I ';' (Stop SCM+FSA)),P,s) = (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA)) )
set s1 = Initialized s;
assume A2: I is_halting_on Initialized s,P ; :: thesis: IExec ((I ';' (Stop SCM+FSA)),P,s) = (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA))
Initialized s = Initialize (Initialized s) by MEMSTR_0:44;
then A4: P +* I halts_on Initialized s by A2, SCMFSA7B:def 7;
( P +* (I ';' (Stop SCM+FSA)) halts_on Initialized s & LifeSpan ((P +* (I ';' (Stop SCM+FSA))),(Initialized s)) = (LifeSpan ((P +* I),(Initialized s))) + 1 ) by A1, A2, Lm4;
then A5: Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s)) = Comput ((P +* (I ';' (Stop SCM+FSA))),(Initialized s),((LifeSpan ((P +* I),(Initialized s))) + 1)) by EXTPRO_1:23;
then DataPart (Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s))) = DataPart (Comput ((P +* I),(Initialized s),(LifeSpan ((P +* I),(Initialized s))))) by A1, A2, Lm4;
then A6: DataPart (Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s))) = DataPart (Result ((P +* I),(Initialized s))) by A4, EXTPRO_1:23
.= DataPart ((Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA))) by MEMSTR_0:79 ;
IC (Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s))) = card I by A1, A2, A5, Lm4
.= IC ((Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA))) by FUNCT_4:113 ;
then A7: Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s)) = (Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA)) by A6, MEMSTR_0:78;
A8: Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s)) = (Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA)) by A7;
thus IExec ((I ';' (Stop SCM+FSA)),P,s) = Result ((P +* (I ';' (Stop SCM+FSA))),(Initialized s)) by SCMFSA6B:def 1
.= (Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA)) by A8
.= (Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA))
.= (Result ((P +* I),(Initialized s))) +* (Start-At ((card I),SCM+FSA))
.= (IExec (I,P,s)) +* (Start-At ((card I),SCM+FSA)) by SCMFSA6B:def 1 ; :: thesis: verum