proposition: Lemma le_not_lt_flip x y : y ≤ x -> ~(x < y).
proof: Proof. intros E1 E2;apply lt_iff_le_apart in E2. destruct E2 as [E2a E2b]. revert E2b. apply tight_apart. apply (antisymmetry (≤));assumption. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.apartness