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_spec: forall {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A} (P: pred A), corable P = forall x y:A, core x = core y -> P x -> P y.