Definition und_ver_assoc {C: predoublecategory_hor_sq} {a b c d : und_ver_cat_ob C} (f: get_und_ver_cat_ob_mor a b) (g: get_und_ver_cat_ob_mor b c) (h: get_und_ver_cat_ob_mor c d) : make_und_ver_cat_comp f (make_und_ver_cat_comp g h) = make_und_ver_cat_comp (make_und_ver_cat_comp f g) h := (und_ver_cat_morphism_eq_principle (make_und_ver_cat_comp f (make_und_ver_cat_comp g h)) (make_und_ver_cat_comp (make_und_ver_cat_comp f g) h) (assoc_hor (pr1 f) (pr1 g) (pr1 h)) (assoc_hor (pr12 f) (pr12 g) (pr12 h)) (assoc_sq_hor (pr22 f) (pr22 g) (pr22 h))).
Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence.