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