proposition: Lemma meet_le x y z : z ≤ x → z ≤ y → z ≤ x ⊓ y.
proof: Proof. intros. rewrite <-(idempotency (⊓) z). now apply meet_le_compat. Qed.
imports: MathClasses.interfaces.abstract_algebra MathClasses.interfaces.orders MathClasses.orders.maps MathClasses.theory.lattices