proposition: Lemma join_r x y : x ≤ y -> x ⊔ y = y.
proof: Proof. intros E. rewrite (commutativity (f:=join)). apply join_l. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.semirings HoTT.Classes.theory.lattices