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_left {B}{A}:
forall (P: B -> pred A) x Q, P x |-- Q -> allp P |-- Q.