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 age_jm_phi: forall {jm jm'}, age jm jm' -> age (m_phi jm) (m_phi jm').