proposition: Lemma from_disp_bicat_of_univ_disp_cats_disp_invertible_2cell_help {C C' : bicat_of_univ_cats} {F : C --> C'} {D : disp_bicat_of_univ_disp_cats C} {D' : disp_bicat_of_univ_disp_cats C'} {FF : D -->[ F ] D'} {GG : D -->[ F ] D'} (αα : FF ==>[ id₂ F ] GG) (H : @is_invertible_2cell bicat_of_univ_cats C C' F F (nat_trans_id _)) (Hαα : is_disp_invertible_2cell H αα) : is_disp_nat_z_iso (nat_z_iso_id _) αα.
proof: Proof. apply from_disp_bicat_of_univ_disp_cats_disp_invertible_2cell. refine (transportf (λ z, is_disp_invertible_2cell z αα) _ Hαα). apply isaprop_is_invertible_2cell. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Fibrations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Adjunctions UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId UniMath.CategoryTheory.DisplayedCats.DisplayedCatEq UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Core.EquivToAdjequiv UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispAdjunctions UniMath.Bicategories.DisplayedBicats.DispInvertibles UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.Examples.FullSub UniMath.Bicategories.DisplayedBicats.Examples.Sigma UniMath.Bicategories.DisplayedBicats.Examples.DisplayedCatToBicat