proposition: Lemma join_l x y : y ≤ x -> x ⊔ y = x.
proof: Proof. intros E. apply (antisymmetry (≤)). - apply join_lub;trivial. apply reflexivity. - apply join_ub_l. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.semirings HoTT.Classes.theory.lattices