proposition: Lemma J_2_0_comp {a : B} : J_2_0 (internal_adjoint_equivalence_identity a) = r a.
proof: Proof. unfold J_2_0. refine (! (!_ @ _)). + exact (J'_2_0_transport _ _ (isotoid_2_0_idtoiso_2_0 HB (idpath a))). + rewrite (functtransportf (idtoiso_2_0 a a) (Y a a)). apply maponpaths_2. exact (homotweqinvweqweq (make_weq (idtoiso_2_0 a a) (HB a a)) (idpath a)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Groupoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Isos UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Unitors UniMath.Bicategories.Core.Invertible_2cells UniMath.Bicategories.Morphisms.Adjunctions UniMath.Bicategories.Core.BicategoryLaws