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 modus_ponens {A} : forall (X P Q:pred A),
X |-- P ->
X |-- (P --> Q) ->
X |-- Q.