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,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(s +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(s +* (Initialize ((intloc 0) .--> 1))))) + 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,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(s +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(s +* (Initialize ((intloc 0) .--> 1))))) + 3))
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))),(s +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(s +* (Initialize ((intloc 0) .--> 1))))) + 3))
let s be State of SCM+FSA; :: thesis: (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(s +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(s +* (Initialize ((intloc 0) .--> 1))))) + 3))
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))),(((StepWhile>0 (a,P,s,I)) . 0) +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(((StepWhile>0 (a,P,s,I)) . 0) +* (Initialize ((intloc 0) .--> 1))))) + 3)) by Def1
.= Comput ((P +* (while>0 (a,I))),(s +* (Initialize ((intloc 0) .--> 1))),((LifeSpan (((P +* (while>0 (a,I))) +* I),(s +* (Initialize ((intloc 0) .--> 1))))) + 3)) by A1 ; :: thesis: verum