proposition: Lemma is_split_monic_to_precomp_is_surjection (m : A --> B) : is_split_monic m -> ∏ c : ob C, issurjective (@precomp_with _ _ _ m c).
proof: Proof. intros is_split c f. apply hinhpr. unfold hfiber, precomp_with. exists (pr1 is_split · f). refine (assoc _ _ _ @ _). refine (maponpaths (fun z => z · _) (pr2 is_split) @ _). apply id_left. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Retracts