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,I,s) . (k + 1) = (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 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,I,s) . (k + 1) = (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 1
let a be read-write Int-Location ; :: thesis: for k being Element of NAT holds (StepWhile=0 a,I,s) . (k + 1) = (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 1
let k be Element of NAT ; :: thesis: (StepWhile=0 a,I,s) . (k + 1) = (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 1
set sk = (StepWhile=0 a,I,s) . k;
set sk0 = (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 ;
(StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 = (StepWhile=0 a,I,s) . k by Def4;
hence (StepWhile=0 a,I,s) . (k + 1) = Comput (ProgramPart (((StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 ) +* ((while=0 a,I) +* (Start-At 0 ,SCM+FSA )))),(((StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 ) +* ((while=0 a,I) +* (Start-At 0 ,SCM+FSA ))),((LifeSpan (ProgramPart (((StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 ) +* (I +* (Start-At 0 ,SCM+FSA )))),(((StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 0 ) +* (I +* (Start-At 0 ,SCM+FSA )))) + 3) by Def4
.= (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . (0 + 1) by Def4
.= (StepWhile=0 a,I,((StepWhile=0 a,I,s) . k)) . 1 ;
:: thesis: verum