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 adr_range_inv: forall loc loc' n, ~ adr_range loc n loc' -> fst loc <> fst loc' \/ (fst loc=fst loc' /\ ~snd loc <= snd loc' < snd loc + n).