proposition: Lemma not_le_lt_flip `{!TrivialApart A} `{DecidablePaths A} x y : ~(y ≤ x) -> x < y.
proof: Proof. intros. destruct (le_or_lt y x); auto. contradiction. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.apartness