Definition jm_update m m' := m_dry m' = m_dry m /\ level m' = level m /\
  resource_at (m_phi m') = resource_at (m_phi m).

Lemma jm_update_age: forall m1 m2 m1', jm_update m1 m2 -> age m1 m1' -> exists m2', jm_update m1' m2' /\ age m2 m2'.