proposition: Lemma total_associator_nat_leftrightwhisker {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dαlrnat : disp_associator_nat_leftrightwhisker dα^{DM}) : associator_nat_leftrightwhisker (total_associatordata dα^{DM}).
proof: Proof. intros x y1 y2 z g. use total2_paths_b. - exact ((associatorlaw_natleftright (monoidal_associatorlaw M)) (pr1 x) (pr1 y1) (pr1 y2) (pr1 z) (pr1 g)). - exact (dαlrnat (pr1 x) (pr1 y1) (pr1 y2) (pr1 z) (pr1 g) (pr2 x) (pr2 y1) (pr2 y2) (pr2 z) (pr2 g)). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors UniMath.CategoryTheory.Monoidal.Displayed.Monoidal UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.Constructions UniMath.CategoryTheory.DisplayedCats.Total