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

Lemma corable_andp_sepcon1{A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}:
forall P Q R, corable P ->  (P && Q) * R = P && (Q * R).