Definition triangle_data_of_duality_inv (x : op2_bicat B) : invertible_2cell (ηinv (L x)) (#L (ηinv x)). Proof. refine (comp_of_invertible_2cell (rinvunitor_invertible_2cell _) _). refine (comp_of_invertible_2cell (lwhisker_of_invertible_2cell _ (psfunctor_id L _)) _). refine (comp_of_invertible_2cell _ (lunitor_invertible_2cell _)). refine (comp_of_invertible_2cell _ (rwhisker_of_invertible_2cell _ (invertible_modcomponent_of unit_inv_unit_of_duality (L x)))). refine (comp_of_invertible_2cell _ (lassociator_invertible_2cell _ _ _)). refine (lwhisker_of_invertible_2cell _ _). refine (comp_of_invertible_2cell _ (rwhisker_of_invertible_2cell _ (inv_of_invertible_2cell (triangle_data_of_duality x)))). refine (comp_of_invertible_2cell _ (inv_of_invertible_2cell (psfunctor_comp L _ _))). use psfunctor_inv2cell. use make_invertible_2cell. - exact (inv_of_invertible_2cell (invertible_modcomponent_of unit_unit_inv_of_duality x)). - use to_op2_is_invertible_2cell. apply property_from_invertible_2cell. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Unitors. Require Import UniMath.Bicategories.Core.BicategoryLaws. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Core.EquivToAdjequiv. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Import PseudoFunctor.Notations. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Op2OfPseudoFunctor. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.Transformations.Examples.Unitality. Require Import UniMath.Bicategories.Transformations.Examples.Associativity. Require Import UniMath.Bicategories.Transformations.Examples.Whiskering. Require Import UniMath.Bicategories.Modifications.Modification. Section CounitFromDualityInvolution. End CounitFromDualityInvolution.