proposition: Lemma cosliced_groupoidal : groupoidal_disp_cat cosliced.
proof: Proof. intros x y f Hf xx yy ff. use tpair. - cbn in *. rewrite <- ff. rewrite assoc'. refine (_ @ id_right _). apply maponpaths. apply (z_iso_inv_after_z_iso (make_z_iso' f Hf)). - split; apply coslice_cat_disp_locally_prop. Qed.
imports: UniMath.MoreFoundations.All UniMath.Foundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Projection UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.coslicecat