reserve a, b, c, a1, a2, b1, b2 for Int-Location,
  l, l1, l2 for Nat,
  f, g, f1, f2 for FinSeq-Location,
  i, j for Instruction of SCM+FSA,
  X, Y for set;
reserve p, r for preProgram of SCM+FSA,
  I, J for Program of SCM+FSA,
  k, m, n for Nat;
reserve L for finite Subset of Int-Locations;

theorem
  a:=b in rng p or AddTo(a, b) in rng p or SubFrom(a, b) in rng p or
  MultBy(a, b) in rng p or Divide(a, b) in rng p implies FirstNotUsed p <> a &
  FirstNotUsed p <> b
proof
  assume a:=b in rng p or AddTo(a, b) in rng p or SubFrom(a, b) in rng p or
  MultBy(a, b) in rng p or Divide(a, b) in rng p;
  then consider i being Instruction of SCM+FSA such that
A1: i in rng p and
A2: i = a:=b or i = AddTo(a, b) or i = SubFrom(a, b) or i = MultBy(a, b
  ) or i = Divide(a, b);
  UsedIntLoc i = {a, b} by A2,Th14;
  then
A3: {a, b} c= UsedILoc p by A1,Th19;
  not FirstNotUsed p in UsedILoc p by Th50;
  hence thesis by A3,ZFMISC_1:32;
end;
