Proposition horizontal_dual_whisker_square_bicat_law : whisker_square_bicat_law horizontal_dual_ver_bicat_sq_id_comp_whisker. Proof. repeat split ; intro ; intros ; cbn. - apply rwhisker_square_id. - apply rwhisker_square_comp. - apply lwhisker_square_id. - apply lwhisker_square_comp. - apply uwhisker_square_id. - apply uwhisker_square_comp. - apply dwhisker_square_id. - apply dwhisker_square_comp. - apply dwhisker_uwhisker_square. - apply rwhisker_uwhisker_square. - apply lwhisker_uwhisker_square. - apply rwhisker_dwhisker_square. - apply lwhisker_dwhisker_square. - refine (!_). apply rwhisker_lwhisker_square. - refine (!_). apply lwhisker_id_h_square. - apply uwhisker_id_v_square. - apply uwhisker_vcomp_square. - apply dwhisker_vcomp_square. - apply ud_whisker_vcomp_square. - apply rwhisker_hcomp_square. - apply lwhisker_hcomp_square. - refine (!_). apply lrwhisker_hcomp_square. Qed.
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.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.OpMorBicat. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.VerityDoubleBicat. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.DerivedLaws. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.CellsAndSquares. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.UnderlyingCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.LocalUnivalence.