Definition is_invertible_2cell_bicat_of_inv2cells {x y : bicat_of_inv2cells} {f g : x --> y} (α : f ==> g) : is_invertible_2cell α. Proof. use make_is_invertible_2cell. - simple refine (_ ,, _). + exact ((pr2 α)^-1). + cbn. is_iso. - abstract (use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; apply vcomp_rinv). - abstract (use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; apply vcomp_linv). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispAdjunctions. Require Import UniMath.Bicategories.DisplayedBicats.DispInvertibles. Require Import UniMath.Bicategories.DisplayedBicats.DispUnivalence.