Lemma resource_decay_joinlist b phi1 phi1' l Phi : rmap_bound b Phi -> resource_decay b phi1 phi1' -> ghost_of phi1' = ghost_fmap (approx (level phi1')) (approx (level phi1')) (ghost_of phi1) -> joinlist (phi1 :: l) Phi -> exists Phi', joinlist (phi1' :: (map (age_to (level phi1')) l)) Phi' /\ resource_decay b Phi Phi' /\ ghost_of Phi' = own.ghost_approx Phi' (ghost_of Phi).