Definition currying_biajd_triangle_r_law: biadj_triangle_r_law currying_biajd_unit_counit. Proof. red. use make_invertible_modification. - intro A. apply nat_z_iso_to_invertible_2cell. use make_nat_z_iso. + use make_nat_trans. * intro G. cbn in G. use make_nat_trans. -- intro b. apply identity. -- intros b b' g. cbn. rewrite id_left, id_right. apply id_right. * intros G G' β. apply (nat_trans_eq (homset_property _)). intro b. cbn. rewrite id_right. apply cancel_postcomposition. apply functor_id. + intro G. apply nat_trafo_z_iso_if_pointwise_z_iso. intro b. cbn. apply identity_is_z_iso. - intros A A' F. apply (nat_trans_eq (homset_property (functor_category _ _))). intro G. cbn. apply (nat_trans_eq (homset_property _)). intro b. cbn. repeat rewrite id_left. repeat rewrite functor_id. repeat rewrite id_left. rewrite id_right. apply pathsinv0, functor_id. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.HorizontalComposition. Require Import UniMath.CategoryTheory.UnitorsAndAssociatorsForEndofunctors. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfCats. Require Import UniMath.Bicategories.PseudoFunctors.Display.PseudoFunctorBicat. Require Import UniMath.Bicategories.PseudoFunctors.PseudoFunctor. Require Import UniMath.Bicategories.PseudoFunctors.Biadjunction. Require Import UniMath.Bicategories.Transformations.PseudoTransformation. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Composition. Require Import UniMath.Bicategories.PseudoFunctors.Examples.Identity. Require Import UniMath.Bicategories.Modifications.Modification. Import Bicat.Notations.