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