proposition: Lemma pseudo_order_embedding_inj `{!StrictOrderEmbedding (f : A -> B)} : IsStrongInjective f.
proof: Proof. split;try apply _. intros x y E. apply apart_iff_total_lt;apply apart_iff_total_lt in E. destruct E; [left | right]; apply (strictly_order_preserving f);trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.orders.orders HoTT.Classes.theory.apartness