Definition doublecategory_to_associator : double_cat_associator Cm. Proof. use make_double_associator. - intros w x y z f g h. use make_iso_twosided_disp. + exact (pr1 (get_ver_associator f g h)). + simple refine (_ ,, _ ,, _). * exact (pr12 (get_ver_associator f g h)). * exact (pr122 (get_ver_associator f g h)). * exact (pr222 (get_ver_associator f g h)). - cbn in *. intros a0 a1 a2 a3 b0 b1 b2 b3 fa fb ha hb ka kb g0 g1 g2 g3 α β γ. exact (! get_predoublecategory_ver_assoc_naturality α β γ). 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.