Program Definition age1_juicy_mem (j: juicy_mem): option juicy_mem :=
      match age1 (m_phi j) with
        | Some phi' => Some (mkJuicyMem (m_dry j) phi' _ _ _ _)
        | None => None
      end.

Lemma rmap_join_sub_eq_level: forall phi1 phi2: rmap, join_sub phi1 phi2 -> level phi1 = level phi2.