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
  b := (f, a) in rng p or (f, a) := b in rng p implies FirstNotUsed p <>
  a & FirstNotUsed p <> b
proof
  assume b := (f, a) in rng p or (f, a) := b in rng p;
  then consider i being Instruction of SCM+FSA such that
A1: i in rng p and
A2: i = b := (f, a) or i = (f, a) := b;
  UsedIntLoc i = {a, b} by A2,Th17;
  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;
