proposition: Lemma join_lt_l_l x y z : z < x -> z < x ⊔ y.
proof: Proof. intros ltzx. refine (lt_le_trans z x _ _ _); try assumption. apply join_ub_l. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.semirings HoTT.Classes.theory.lattices