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;
