let s be State of SCM+FSA; :: thesis: for I being Program of SCM+FSA
for a being read-write Int-Location
for k being Element of NAT
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT holds (StepWhile>0 (a,P,s,I)) . (k + 1) = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1
let I be Program of SCM+FSA; :: thesis: for a being read-write Int-Location
for k being Element of NAT
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT holds (StepWhile>0 (a,P,s,I)) . (k + 1) = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1
let a be read-write Int-Location ; :: thesis: for k being Element of NAT
for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT holds (StepWhile>0 (a,P,s,I)) . (k + 1) = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1
let k be Element of NAT ; :: thesis: for P being the Instructions of SCM+FSA -valued ManySortedSet of NAT holds (StepWhile>0 (a,P,s,I)) . (k + 1) = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1
let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: (StepWhile>0 (a,P,s,I)) . (k + 1) = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1
set sk = (StepWhile>0 (a,P,s,I)) . k;
set sk0 = (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 0;
(StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 0 = (StepWhile>0 (a,P,s,I)) . k by Def1;
hence (StepWhile>0 (a,P,s,I)) . (k + 1) = Comput ((P +* (while>0 (a,I))),(((StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 0) +* (Initialized (while>0 (a,I)))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(((StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 0) +* (Initialized I)))) + 3)) by Def1
.= (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . (0 + 1) by Def1
.= (StepWhile>0 (a,P,((StepWhile>0 (a,P,s,I)) . k),I)) . 1 ;
:: thesis: verum