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_allp {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{agA: ageable A}{AgeA: Age_alg A}:
forall {B: Type} (P:  B -> pred A) ,
(forall b, corable (P b)) -> corable (allp P).