let P be Instruction-Sequence of SCM+FSA; :: thesis: for I being Program of
for a being read-write Int-Location
for s being State of SCM+FSA holds (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(Initialize s),((LifeSpan (((P +* (while=0 (a,I))) +* I),(Initialize s))) + 3))

let I be Program of ; :: thesis: for a being read-write Int-Location
for s being State of SCM+FSA holds (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(Initialize s),((LifeSpan (((P +* (while=0 (a,I))) +* I),(Initialize s))) + 3))

let a be read-write Int-Location ; :: thesis: for s being State of SCM+FSA holds (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(Initialize s),((LifeSpan (((P +* (while=0 (a,I))) +* I),(Initialize s))) + 3))
let s be State of SCM+FSA; :: thesis: (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(Initialize s),((LifeSpan (((P +* (while=0 (a,I))) +* I),(Initialize s))) + 3))
A1: (StepWhile=0 (a,I,P,s)) . 0 = s by Def4;
thus (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(Initialize s),((LifeSpan (((P +* (while=0 (a,I))) +* I),(Initialize s))) + 3)) by A1, Def4; :: thesis: verum