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_mapped_inj: forall f m1 m2 b1 b2 delta lo hi p m1', mem_inj f m1 m2 -> drop_perm m1 b1 lo hi p = Some m1' -> meminj_no_overlap f m1 -> f b1 = Some(b2, delta) -> exists m2', drop_perm m2 b2 (lo + delta) (hi + delta) p = Some m2' /\ mem_inj f m1' m2'.