Local Open Scope pred.
Definition corable {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}
(P: pred A) := forall w, P w = P (core w).

Lemma corable_sepcon_andp1 {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}:
forall P Q R, corable P ->  Q  * (P && R) = P && (Q * R).