Definition invertible_2cell_to_vertical_square {x y : B} {v₁ v₂ : x -|-> y} (τ : invertible_2cell v₁ v₂) : invertible_vertical_square v₁ v₂. Proof. use make_invertible_vertical_square. - use make_invertible_vertical_square_data. + exact (vertical_cell_to_square τ). + exact (vertical_cell_to_square (τ^-1)). - split. + abstract (cbn -[comp_ver_globular_square] ; refine (_ @ vertical_cell_to_square_id _) ; rewrite <- vertical_cell_to_square_comp ; apply maponpaths ; apply (vcomp_rinv τ)). + abstract (cbn -[comp_ver_globular_square] ; refine (_ @ vertical_cell_to_square_id _) ; rewrite <- vertical_cell_to_square_comp ; apply maponpaths ; apply (vcomp_linv τ)). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws.