Lemma total_leftunitor_nat {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dluiso : disp_leftunitor_nat dlu^{DM}) : leftunitor_nat (total_leftunitordata dlu^{DM}). Proof. intros x y f. use total2_paths_b. - exact ((pr1 (monoidal_leftunitorlaw M)) (pr1 x) (pr1 y) (pr1 f)). - exact (dluiso (pr1 x) (pr1 y) (pr1 f) (pr2 x) (pr2 y) (pr2 f)). Defined.
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.