extensionality a.  apply prop_ext. split; repeat intro.
destruct H0 as [a' ?]. unfold full in H.
specialize (H a'). spec H...
destruct H0 as [c ?].
specialize (H c). spec H... subst. apply join_comm in H0.
apply no_units in H0. contradiction.
Qed.

(* Specifications: *)
Lemma psub_joins {A}  {JA: Join A} {PA: Perm_alg A} {Pos_A: Pos_alg A}{DA: Disj_alg A} : forall a b,
join_sub a b -> joins a b -> False.