Ltac hered :=
  match goal with
    H : ?P ?x |- ?P ?y => revert H
  end;
  match goal with
    |- ?P ?x -> ?P ?y =>
    cut (hereditary age P);
    [ let h := fresh "h" in intros h; apply h; auto | ]
  end.Ltac agejoinhyp :=
  match goal with
    H : sepalg.join _ _ ?m, A : age ?m _ |- _ =>
    pose proof age1_join2 _ H A; clear H
  end.Ltac agehyps :=
  match goal with
    H : age ?x ?y, HH : ?P ?x |- _ =>
    cut (P y);
    [ clear HH; intros HH
    | hered;
      try apply pred_hered;
      try apply predicates_hered.exactly_obligation_1]
  end.

Lemma m_phi_age_to n jm : m_phi (age_to n jm) = age_to n (m_phi jm).