proposition: Lemma iso_to_dispadjequiv (C : bicat_of_univ_cats) (IC ID : bidisp_unit_disp_bicat C) : z_iso IC ID -> disp_adjoint_equivalence (idtoiso_2_0 C C (idpath C)) IC ID.
proof: Proof. intro i. induction i as [finv [f [li ri]]]. split with f. unfold disp_left_adjoint_equivalence. repeat (use tpair); try apply univalent_category_has_homsets. - exact finv. - etrans. { apply id_left. } exact (! li). - etrans. { apply cancel_postcomposition. apply ri. } apply id_right. - etrans. { apply cancel_postcomposition. apply li. } apply id_left. - etrans. { apply id_left. } exact (! ri). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Total UniMath.Bicategories.Core.Bicat UniMath.Bicategories.Core.Examples.BicatOfUnivCats UniMath.Bicategories.DisplayedBicats.DispBicat UniMath.Bicategories.DisplayedBicats.DispUnivalence UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories