Definition superprecise {A}  {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A} (P: pred A) :=
forall w1 w2, P w1 -> P w2 -> comparable w1 w2 -> w1=w2.

Lemma allp_derives_right {A} : forall B p (q: B -> pred A),
((p |-- allp q) <-> (forall x, p |-- q x)).