proposition: Lemma total_associator_iso_law {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dαiso : disp_associator_iso dα^{DM} dαinv^{DM}) : associator_iso_law (total_associatordata dα^{DM}) (total_associatorinvdata dαinv^{DM}).
proof: Proof. intros x y z. - split. + use total2_paths_b. * exact (pr1 (associatorlaw_iso_law (monoidal_associatorlaw M) (pr1 x) (pr1 y) (pr1 z))). * exact (pr2 ((dαiso) (pr1 x) (pr1 y) (pr1 z) (pr2 x) (pr2 y) (pr2 z))). + use total2_paths_b. * exact (pr2 (associatorlaw_iso_law (monoidal_associatorlaw M) (pr1 x) (pr1 y) (pr1 z))). * exact (pr1 ((dαiso) (pr1 x) (pr1 y) (pr1 z) (pr2 x) (pr2 y) (pr2 z))). 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