proposition: Lemma SplitEpis_HSET : AxiomOfChoice_surj -> epis_are_split HSET.
proof: Proof. intros axC A B f epif. apply EpisAreSurjective_HSET,axC in epif. unshelve eapply (hinhfun _ epif). intro h. exists (pr1 h). apply funextfun. exact (pr2 h). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.AxiomOfChoice UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.slicecat UniMath.CategoryTheory.NNO UniMath.CategoryTheory.SubobjectClassifier UniMath.CategoryTheory.Categories.Type.Core UniMath.CategoryTheory.Categories.Type.MonoEpiIso UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.covyoneda UniMath.CategoryTheory.EpiFacts UniMath.CategoryTheory.Monics UniMath.CategoryTheory.SplitMonicsAndEpis UniMath.CategoryTheory.ElementaryTopos UniMath.CategoryTheory.PowerObject UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.Limits UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.Categories.HSET.Univalence