Lemma total_associator_law {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dαiso : disp_associator_law dα^{DM} dαinv^{DM}) : associator_law (total_associatordata dα^{DM}) (total_associatorinvdata dαinv^{DM}). Proof. split with (total_associator_nat_leftwhisker (disp_associatorlaw_natleft dαiso)). split with (total_associator_nat_rightwhisker (disp_associatorlaw_natright dαiso)). split with (total_associator_nat_leftrightwhisker (disp_associatorlaw_natleftright dαiso)). exact (total_associator_iso_law (disp_associatorlaw_iso dαiso)). 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.