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 level2_juicy_mem: forall j1 j2: juicy_mem, age1_juicy_mem j1 = Some j2 -> level (m_phi j1) = S (level (m_phi j2)).