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,s,I)) . (0 + 1) = Comput ((ProgramPart (s +* (Initialized (while>0 (a,I))))),(s +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (s +* (Initialized I))),(s +* (Initialized I)))) + 3))
let a be read-write Int-Location ; :: thesis: for s being State of SCM+FSA holds (StepWhile>0 (a,s,I)) . (0 + 1) = Comput ((ProgramPart (s +* (Initialized (while>0 (a,I))))),(s +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (s +* (Initialized I))),(s +* (Initialized I)))) + 3))
let s be State of SCM+FSA; :: thesis: (StepWhile>0 (a,s,I)) . (0 + 1) = Comput ((ProgramPart (s +* (Initialized (while>0 (a,I))))),(s +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (s +* (Initialized I))),(s +* (Initialized I)))) + 3))
X: (StepWhile>0 (a,s,I)) . 0 = s by Def1;
thus (StepWhile>0 (a,s,I)) . (0 + 1) = Comput ((ProgramPart (((StepWhile>0 (a,s,I)) . 0) +* (Initialized (while>0 (a,I))))),(((StepWhile>0 (a,s,I)) . 0) +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (((StepWhile>0 (a,s,I)) . 0) +* (Initialized I))),(((StepWhile>0 (a,s,I)) . 0) +* (Initialized I)))) + 3)) by Def1
.= Comput ((ProgramPart (s +* (Initialized (while>0 (a,I))))),(s +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (((StepWhile>0 (a,s,I)) . 0) +* (Initialized I))),(((StepWhile>0 (a,s,I)) . 0) +* (Initialized I)))) + 3)) by X
.= Comput ((ProgramPart (s +* (Initialized (while>0 (a,I))))),(s +* (Initialized (while>0 (a,I)))),((LifeSpan ((ProgramPart (s +* (Initialized I))),(s +* (Initialized I)))) + 3)) by X ; :: thesis: verum