theorem
  UsedILoc(p +* r) c= UsedILoc p \/ UsedILoc r
proof
   rng(p +* r) c= rng p \/ rng r by FUNCT_4:17;
   then UsedILoc(p +* r) c= UsedILoc(rng p \/ rng r) by Lm2;
  hence UsedILoc(p +* r) c= UsedILoc p \/ UsedILoc r by Lm3;
end;
