let P be 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 holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))
let I be MacroInstruction of SCM+FSA ; for a being read-write Int-Location
for s being State of SCM+FSA holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))
let a be read-write Int-Location; for s being State of SCM+FSA holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))
let s be State of SCM+FSA; (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))
A1:
(StepWhile>0 (a,P,s,I)) . 0 = s
by Def1;
thus (StepWhile>0 (a,P,s,I)) . (0 + 1) =
Comput ((P +* (while>0 (a,I))),(Initialized ((StepWhile>0 (a,P,s,I)) . 0)),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized ((StepWhile>0 (a,P,s,I)) . 0)))) + 2))
by Def1
.=
Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))
by A1
; verum