let P be the Instructions of SCM+FSA -valued ManySortedSet of NAT ; :: thesis: for I being Program of SCM+FSA
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))),(s +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(s +* (Initialize I)))) + 3))
let I be Program of SCM+FSA; :: 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))),(s +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(s +* (Initialize I)))) + 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))),(s +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(s +* (Initialize I)))) + 3))
let s be State of SCM+FSA; :: thesis: (StepWhile=0 (a,I,P,s)) . (0 + 1) = Comput ((P +* (while=0 (a,I))),(s +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(s +* (Initialize I)))) + 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))),(((StepWhile=0 (a,I,P,s)) . 0) +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(((StepWhile=0 (a,I,P,s)) . 0) +* (Initialize I)))) + 3)) by Def4
.= Comput ((P +* (while=0 (a,I))),(s +* (Initialize (while=0 (a,I)))),((LifeSpan (((P +* (while=0 (a,I))) +* I),(s +* (Initialize I)))) + 3)) by A1 ; :: thesis: verum