Definition doublecategory_to_runitor : double_cat_runitor I Cm. Proof. use make_double_runitor. - intros x y h. use make_iso_twosided_disp. + cbn in *. exact (pr1 (get_ver_right_unitor h)). + simple refine (_ ,, _ ,, _). * exact (pr12 (get_ver_right_unitor h)). * cbn in *. exact (pr122 (get_ver_right_unitor h)). * exact (pr222 (get_ver_right_unitor h)). - cbn in *. intros a b c d f g h k α. exact (! get_predoublecategory_ver_right_unitor_naturality α). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.BicatOfDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.AlternativeDefinitions.DoubleCatsUnfolded.