Lemma total_rightunitor_iso_law {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (druiso : disp_rightunitor_iso dru^{DM} druinv^{DM}) : rightunitor_iso_law (total_rightunitordata dru^{DM}) (total_rightunitorinvdata druinv^{DM}). Proof. intros x. split. - use total2_paths_b. + exact (pr1 (pr2 (monoidal_rightunitorlaw M) (pr1 x))). + exact (pr2 (druiso (pr1 x) (pr2 x))). - use total2_paths_b. * exact (pr2 (pr2 (monoidal_rightunitorlaw M) (pr1 x))). * exact (pr1 (druiso (pr1 x) (pr2 x))). 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.