Arguments resource_at_empty [phi] _ _.
Ltac inj_pair_tac :=
match goal with H: (@existT ?U ?P ?p ?x = @existT _ _ _ ?y) |- _ =>
generalize (@inj_pair2 U P p x y H); clear H; intro; try (subst x || subst y)
end.

Lemma age1_PURE: forall phi phi' l k ,
age1 phi = Some phi' -> ((exists P, phi @ l = PURE k P) <-> exists P, phi' @ l = PURE k P).