Definition invertible_2cell_to_horizontal_square {x y : B} {h₁ h₂ : x --> y} (τ : invertible_2cell h₁ h₂) : invertible_horizontal_square h₁ h₂. Proof. use make_invertible_horizontal_square. - use make_invertible_horizontal_square_data. + exact (horizontal_cell_to_square τ). + exact (horizontal_cell_to_square (τ^-1)). - split. + abstract (cbn -[comp_hor_globular_square] ; refine (_ @ horizontal_cell_to_square_id _) ; rewrite <- horizontal_cell_to_square_comp ; apply maponpaths ; exact (vcomp_rinv τ)). + abstract (cbn -[comp_hor_globular_square] ; refine (_ @ horizontal_cell_to_square_id _) ; rewrite <- horizontal_cell_to_square_comp ; apply maponpaths ; exact (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.