Definition mod_after_alloc (phi: rmap) (lo hi: Z) (b: block) :=
  proj1_sig (make_rmap (mod_after_alloc' phi lo hi b) (ghost_of phi)
    _
    (mod_after_alloc'_ok phi lo hi b) (ghost_of_approx phi)).

Lemma fullempty_after_alloc : forall m1 m2 lo n b ofs, alloc m1 lo n = (m2, b) -> access_at m2 (b, ofs) Cur = None \/ access_at m2 (b, ofs) Cur = Some Freeable.