let P be Instruction-Sequence of SCM+FSA; for s being State of SCM+FSA
for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location
for k being Nat 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
for k being Nat 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
for k being Nat 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; for k being Nat 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; (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 Def1;
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 Def1
.=
(StepWhile=0 (a,I,P,((StepWhile=0 (a,I,P,s)) . k))) . (0 + 1)
by Def1
.=
(StepWhile=0 (a,I,P,((StepWhile=0 (a,I,P,s)) . k))) . 1
;
verum