Definition square_verity_double_ver_inv2cell_weq {x y : B} (f g : x --> y) : invertible_2cell (C := B) f g ≃ invertible_2cell (C := ver_bicat_of_verity_double_bicat square_verity_double_bicat) f g. Proof. use weq_iso. - exact square_verity_double_to_ver_inv2cell. - exact square_verity_double_from_ver_inv2cell. - abstract (intro τ ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; apply idpath). - abstract (intro τ ; use subtypePath ; [ intro ; apply isaprop_is_invertible_2cell | ] ; apply idpath). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core.