Definition currying_biajd_triangle_l_law: biadj_triangle_l_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 ab. apply identity. * intros ab ab' fg. cbn. apply pathsdirprod. -- rewrite id_right. apply idpath. -- rewrite id_left. rewrite id_right. apply id_right. + intro ab. cbn. set (aux := identity(C:=pr1(productwithfixedelement _ _)) ab). change (is_z_isomorphism aux). apply identity_is_z_iso. - intros A A' F. apply (nat_trans_eq (homset_property (productwithfixedelement _ _))). intro ab. cbn. apply pathsdirprod. + rewrite functor_id. repeat rewrite id_left. apply idpath. + repeat rewrite id_left. apply idpath. 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.