Definition square_vertically_saturated : vertically_saturated square_verity_double_bicat. Proof. intros x y v₁ v₂. use isweq_iso. - exact (λ τ, linvunitor _ • τ • runitor _). - abstract (intros τ ; cbn ; rewrite !vassocr ; rewrite linvunitor_lunitor ; rewrite id2_left ; rewrite !vassocl ; rewrite vcomp_runitor ; rewrite !vassocr ; rewrite rinvunitor_runitor ; apply id2_left). - abstract (intros τ ; cbn ; rewrite rwhisker_hcomp ; rewrite !vassocl ; rewrite <- rinvunitor_natural ; rewrite !vassocl ; rewrite runitor_rinvunitor ; rewrite id2_right ; rewrite !vassocr ; rewrite lunitor_linvunitor ; apply id2_left). 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.