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;

theorem Th21:
  dom p misses dom r implies
   UsedILoc(p +* r) = UsedILoc p \/ UsedILoc r
proof
 assume dom p misses dom r;
  then rng(p +* r) = rng p \/ rng r by NECKLACE:6;
  then UsedILoc(p +* r) = UsedILoc(rng p \/ rng r);
 hence UsedILoc(p +* r) = UsedILoc p \/ UsedILoc r by Lm3;
end;
