reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,j,k,n for Nat;
reserve P,P1,P2,Q for Instruction-Sequence of SCM+FSA;

theorem Th8:
  for I being MacroInstruction of SCM+FSA,a being read-write Int-Location,
  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)
proof
  let I be MacroInstruction of SCM+FSA,a be read-write Int-Location,
      s be State of SCM+FSA;
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;
end;
