proposition: Lemma below_bottom x : x ≤ ⊥ -> x = ⊥.
proof: Proof. intros E. apply join_sl_le_spec in E. rewrite right_identity in E. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.semirings HoTT.Classes.theory.lattices