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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))

let s be State of SCM+FSA; :: thesis: (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2)) by A1 ; :: thesis: verum

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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2))

let s be State of SCM+FSA; :: thesis: (StepWhile>0 (a,P,s,I)) . (0 + 1) = Comput ((P +* (while>0 (a,I))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 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))),(Initialized s),((LifeSpan (((P +* (while>0 (a,I))) +* I),(Initialized s))) + 2)) by A1 ; :: thesis: verum