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_zle_fact : forall b lo hi loc, adr_range (b,lo) (hi-lo) loc -> zle lo (snd loc) && zlt (snd loc) hi = true.