Proposition rassociator_h_coreflections_path {C : two_cat} {HC : locally_univalent_two_cat C} {w x y z : coreflections_double_cat C HC} (h₁ : w -->h x) (h₂ : x -->h y) (h₃ : y -->h z) : ((h₁ ·h h₂) ·h h₃) · pr1 (identity_v z) = pr1 (identity_v w) · (h₁ ·h (h₂ ·h h₃)). Proof. cbn. rewrite (id_right (C := C)). rewrite (id_left (C := C)). apply (assoc' (C := C)). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.Core.TwoCategories. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Examples.Sigma. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Strictness. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Examples.SquaresTwoCat. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.Strictness. Require Import UniMath.Bicategories.Core.AdjointUnique. Require Import UniMath.Bicategories.Morphisms.Adjunctions. Require Import UniMath.Bicategories.Morphisms.Properties.Composition. Require Import UniMath.Bicategories.DoubleCategories.Basics.StrictDoubleCatBasics. Require Import UniMath.Bicategories.DoubleCategories.Basics.DoubleCategoryBasics. Require Import UniMath.Bicategories.DoubleCategories.Core.DoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.UnivalentDoubleCats. Require Import UniMath.Bicategories.DoubleCategories.Core.PseudoDoubleSetCats. Require Import UniMath.Bicategories.DoubleCategories.Core.CompanionsAndConjoints. Require Import UniMath.Bicategories.DoubleCategories.Examples.SquareDoubleCatTwo. Require Import UniMath.Bicategories.DoubleCategories.Examples.DoubleCatOnDispCat. Import TwoCategories.Notations.