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