Set Bullet Behavior "Strict Subproofs".
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.
(** * Aging and predicates *)
(** * Aging and operational steps *)

Lemma jsafeN__age {G C Z HH Sem Jspec ge ora q n} jm jmaged :
ext_spec_stable age (JE_spec _ Jspec) ->
age jm jmaged ->
le n (level jmaged) ->
@jsafeN_ G Z C HH Sem Jspec ge n ora q jm ->
@jsafeN_ G Z C HH Sem Jspec ge n ora q jmaged.