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