Definition pure {A}{JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}
(P: pred A) : Prop :=
P |-- emp.

Lemma pure_sepcon {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}: forall (P : pred A), pure P -> P*P=P.