proposition: Lemma join_l x y : y ≤ x → x ⊔ y = x.
proof: Proof. intros E. apply (antisymmetry (≤)). now apply join_lub. apply join_ub_l. Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices