proposition: Lemma meet_join_distr_l_le x y z : (x ⊓ y) ⊔ (x ⊓ z) ≤ x ⊓ (y ⊔ z).
proof: Proof. apply meet_le. apply join_le; now apply meet_lb_l. apply join_le. transitivity y. apply meet_lb_r. apply join_ub_l. transitivity z. apply meet_lb_r. apply join_ub_r. Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices