let P be Instruction-Sequence of SCM+FSA; :: thesis: for I being MacroInstruction of SCM+FSA
for a being read-write Int-Location
for s being State of SCM+FSA holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(),((LifeSpan (((P +* (while>0 (a,I))) +* I),())) + 2))

let I be MacroInstruction of SCM+FSA ; :: thesis: for a being read-write Int-Location
for s being State of SCM+FSA holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(),((LifeSpan (((P +* (while>0 (a,I))) +* I),())) + 2))

let a be read-write Int-Location; :: thesis: for s being State of SCM+FSA holds (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(),((LifeSpan (((P +* (while>0 (a,I))) +* I),())) + 2))
let s be State of SCM+FSA; :: thesis: (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(),((LifeSpan (((P +* (while>0 (a,I))) +* I),())) + 2))
A1: (StepWhile>0 (a,P,s,I)) . 0 = s by Def1;
thus (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized ((StepWhile>0 (a,P,s,I)) . 0)),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized ((StepWhile>0 (a,P,s,I)) . 0)))) + 2)) by Def1
.= Comput ((P +* (while>0 (a,I))),(),((LifeSpan (((P +* (while>0 (a,I))) +* I),())) + 2)) by A1 ; :: thesis: verum