(* Disj_alg: adds the property that no nonempty element can join with itself. *)
Class Disj_alg  (t: Type) {J: Join t} :=
   join_self: forall {a b}, join a a b -> identity a.(* Disj_alg: adds the property that no nonempty element can join with itself. *)
Class Disj_alg  (t: Type) {J: Join t} :=
   join_self: forall {a b}, join a a b -> identity a.

Lemma unit_identity {A}{J: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{CA: Disj_alg A} : forall {e} b, unit_for e b -> identity e.