Definition identity_rmap' : R.rmap' := exist valid (fun _: AV.address => R.NO) AV.valid_empty.Definition identity_rmap (n:nat) : rmap := R.squash (n, identity_rmap').

Lemma ageN_level : forall n (phi1 phi2 : rmap), ageN n phi1 = Some phi2 -> level phi1 = (n + (level phi2))%nat.