proposition: Lemma hfiber_in_hfiber : ∏ Z W (g : Z -> W) (w : W) (z : hfiber g w), hfiber g (g (hfiberpr1 _ _ z)).
proof: Proof. intros. use make_hfiber. - exact (hfiberpr1 _ _ z). - apply idpath. Defined.
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