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 exists_expand_and {A} {JA: Join A}: forall B (p: B -> pred A) q, (exp p && q)%pred = (exp (fun x => p x && q))%pred.