reserve s, s1, s2 for State of SCM+FSA,
  p, p1 for Instruction-Sequence of SCM+FSA,
  a, b for Int-Location,
  d for read-write Int-Location,
  f for FinSeq-Location,
  I for MacroInstruction of SCM+FSA,
  J for good MacroInstruction of SCM+FSA,
  k, m for Nat;

theorem
  UsedI*Loc times(b, I) = UsedI*Loc I
proof
  set a = b;
  set aux = 1-stRWNotIn ({a} \/ UsedILoc I);
  thus UsedI*Loc times(a,I) = UsedInt*Loc(aux := a)\/ UsedI*Loc while>0(
  aux,I ";" SubFrom(aux, intloc 0)) by SF_MASTR:45
    .= {} \/ UsedI*Loc while>0(aux, I ";" SubFrom(aux, intloc 0)) by
SF_MASTR:32
    .= UsedI*Loc (I ";" SubFrom(aux,intloc 0)) by SCMFSA9A:25
    .= (UsedI*Loc I) \/ UsedInt*Loc SubFrom(aux, intloc 0) by SF_MASTR:46
    .= (UsedI*Loc I) \/ {} by SF_MASTR:32
    .= UsedI*Loc I;
end;
