proposition: Lemma join_le_compat_r x y z : z ≤ x → z ≤ x ⊔ y.
proof: Proof. intros E. transitivity x. easy. apply join_ub_l. Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices