proposition: Lemma join_le_compat_l x y z : z ≤ y → z ≤ x ⊔ y.
proof: Proof. intros E. rewrite commutativity. now apply join_le_compat_r. Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices