Hint Resolve @pure_con'.

(* Specifications: *)
Lemma pure_intersection1: forall {A}  {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}
(P Q: pred A), pure P -> pure (P && Q).
Lemma pure_intersection2: forall {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}
(P Q: pred A), pure Q -> pure (P && Q).