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_sepcon {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}:
forall P Q, corable P -> corable Q -> corable (P * Q).