theorem Th37:
  dom p misses dom r implies UsedI*Loc (p +* r) = (UsedI*Loc p
  ) \/ (UsedI*Loc r)
proof
 assume dom p misses dom r;
  then rng(p +* r) = rng p \/ rng r by NECKLACE:6;
  then UsedI*Loc(p +* r) = UsedI*Loc(rng p \/ rng r);
 hence UsedI*Loc(p +* r) = UsedI*Loc p \/ UsedI*Loc r by Lm6;
end;
