theorem Th9: :: SCMISORT:14

for P being Instruction-Sequence of SCM+FSA
for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location
for s being State of SCM+FSA
for k, n being Nat st IC ((StepWhile>0 (a,P,s,I)) . k) = 0 & (StepWhile>0 (a,P,s,I)) . k = Comput ((P +* (while>0 (a,I))),(Initialized s),n) & ((StepWhile>0 (a,P,s,I)) . k) . (intloc 0) = 1 holds
( (StepWhile>0 (a,P,s,I)) . k = Initialized ((StepWhile>0 (a,P,s,I)) . k) & (StepWhile>0 (a,P,s,I)) . (k + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),(n + ((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized ((StepWhile>0 (a,P,s,I)) . k)))) + 2))) )