Definition nonidentity {A} `{Perm_alg A} (a: A) := ~(identity a).

Lemma join_sub_units_eq {A} {J: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{CA: Disj_alg A} : forall {a b} ea eb, join_sub a b -> unit_for ea a -> unit_for eb b -> ea = eb.