Definition meminj_no_overlap (f: meminj) (m: mem) : Prop :=
  forall b1 b1' delta1 b2 b2' delta2 ofs1 ofs2,
  b1 <> b2 ->
  f b1 = Some (b1', delta1) ->
  f b2 = Some (b2', delta2) ->
  perm m b1 ofs1 Max Nonempty ->
  perm m b2 ofs2 Max Nonempty ->
  b1' <> b2' \/ ofs1 + delta1 <> ofs2 + delta2.

Lemma drop_outside_inj: forall f m1 m2 b lo hi p m2', mem_inj f m1 m2 -> drop_perm m2 b lo hi p = Some m2' -> (forall b' delta ofs' k p, f b' = Some(b, delta) -> perm m1 b' ofs' k p -> lo <= ofs' + delta < hi -> False) -> mem_inj f m1 m2'.