proposition: Lemma adjoint_equivalence_rinv (a b : B) (f : adjoint_equivalence a b) : comp_adjoint_equivalence a b a f (inv_adjoint_equivalence a b f) = internal_adjoint_equivalence_identity a.
proof: Proof. apply (J_2_0 HB (λ a b f, comp_adjoint_equivalence a b a f (inv_adjoint_equivalence a b f) = internal_adjoint_equivalence_identity a)). intro c. rewrite adjoint_equivalence_lid. unfold inv_adjoint_equivalence. rewrite J_2_0_comp. exact (idpath _). 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