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 find_overlap {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}:
Cross_alg A ->
forall S P Q R, (S * P) && (Q * R) |--
EX SQ:_, EX SR:_, EX PQ:_, EX PR:_,
(((SQ* SR) && S)*((PQ* PR) && P)) &&
(((SQ* PQ) && Q)*((SR* PR) && R)) &&
!! (superprecise SQ /\ superprecise SR /\ superprecise PQ /\ superprecise PR).