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

Lemma joins_units_eq {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{CA: Disj_alg A}: forall {a b} ea eb, joins a b -> unit_for ea a -> unit_for eb b -> ea = eb.