Lemma total_triangleidentity {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dti : disp_triangle_identity dlu^{DM} dru^{DM} dα^{DM}) : triangle_identity (total_leftunitordata dlu^{DM}) (total_rightunitordata dru^{DM}) (total_associatordata dα^{DM}). Proof. intros x y. use total2_paths_b. - exact ((monoidal_triangleidentity M) (pr1 x) (pr1 y)). - exact (dti (pr1 x) (pr1 y) (pr2 x) (pr2 y)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Import BifunctorNotations. Import MonoidalNotations. Import DisplayedBifunctorNotations. Import DisplayedMonoidalNotations.