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