proposition: Lemma meet_le_compat_l x y z : y ≤ z -> x ⊓ y ≤ z.
proof: Proof. intros E. rewrite (commutativity (f:=meet)). apply meet_le_compat_r. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.semirings HoTT.Classes.theory.lattices