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