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_decay_trans: forall b b' m1 m2 m3, (b <= b')%positive -> resource_decay b m1 m2 -> resource_decay b' m2 m3 -> resource_decay b m1 m3.