proposition: Lemma z_iso_to_slice_precat_z_iso (af bg : C / x) (h : af --> bg) (isoh : is_z_isomorphism (pr1 h)) : is_z_isomorphism h.
proof: Proof. induction isoh as [hinv [h1 h2]]. assert (pinv : hinv · pr2 af = pr2 bg). { rewrite <- id_left, <- h2, <- assoc, (!(pr2 h)); apply idpath. } exists (hinv,,!pinv). split; (apply subtypePairEquality; [ intro; apply C |]); assumption. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Univalence UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.exponentials UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis