reserve P,Q for Instruction-Sequence of SCM+FSA;
reserve m, n for Nat;
reserve f for FinSeq-Location,
  c for Int-Location;
reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;
reserve i,k,m,n for Nat;
reserve s for State of SCM+FSA,
  I for MacroInstruction of SCM+FSA,
  a for read-write Int-Location;

theorem Th17:
  for I being MacroInstruction of SCM+FSA,a being read-write Int-Location,
  s being State of SCM+FSA holds StepWhile>0(a,I,P,s).1
  = Comput(P +* while>0(a,I),
       Initialize s,
       LifeSpan(P +* while>0(a,I)+* I,Initialize 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,I,P,s).0 = s by Def2;
  thus StepWhile>0(a,I,P,s).1 = StepWhile>0(a,I,P,s).(0+1)
   .= Comput(P +* while>0(a,I), (Initialize s),
    (LifeSpan(P +* while>0(a,I)+* I,Initialize s)+ 2)) by A1,Def2;
end;
