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 resource_nodecay_decay: forall b phi1 phi2, resource_nodecay b phi1 phi2 -> resource_decay b phi1 phi2.