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;

theorem Th5:
  StepWhile=0(a,I,P,s).(k+1)=StepWhile=0(a,I,P,StepWhile=0(a,I,P,s).k).1
proof
  set sk=StepWhile=0(a,I,P,s).k;
  set sk0=StepWhile=0(a,I,P,sk).0;
  sk0=sk by Def1;
  hence
  StepWhile=0(a,I,P,s).(k+1) = Comput(P +*while=0(a,I), Initialize sk0,
  (LifeSpan(P +*while=0(a,I) +* I,Initialize sk0) + 2)) by Def1
    .=StepWhile=0(a,I,P,sk).(0+1) by Def1
    .=StepWhile=0(a,I,P,sk).1;
end;
