let P be Instruction-Sequence of SCM+FSA; for k being Nat
for s being State of SCM+FSA
for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location holds (StepWhile>0 (a,I,P,s)) . (k + 1) = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
let k be Nat; for s being State of SCM+FSA
for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location holds (StepWhile>0 (a,I,P,s)) . (k + 1) = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
let s be State of SCM+FSA; for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location holds (StepWhile>0 (a,I,P,s)) . (k + 1) = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
let I be MacroInstruction of SCM+FSA ; for a being read-write Int-Location holds (StepWhile>0 (a,I,P,s)) . (k + 1) = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
let a be read-write Int-Location; (StepWhile>0 (a,I,P,s)) . (k + 1) = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
set sk = (StepWhile>0 (a,I,P,s)) . k;
set sk0 = (StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 0;
(StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 0 = (StepWhile>0 (a,I,P,s)) . k
by Def2;
hence (StepWhile>0 (a,I,P,s)) . (k + 1) =
Comput ((P +* (while>0 (a,I))),(Initialize ((StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 0)),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialize ((StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 0)))) + 2))
by Def2
.=
(StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . (0 + 1)
by Def2
.=
(StepWhile>0 (a,I,P,((StepWhile>0 (a,I,P,s)) . k))) . 1
;
verum