proposition: Lemma total_pentagonidentity {C : category} {D : disp_cat C} {M : monoidal C} {DM : disp_monoidal_data D M} (dpi : disp_pentagon_identity dα^{DM}) : pentagon_identity (total_associatordata dα^{DM}).
proof: Proof. intros w x y z. use total2_paths_b. - exact ((monoidal_pentagonidentity M) (pr1 w) (pr1 x) (pr1 y) (pr1 z)). - exact (dpi (pr1 w) (pr1 x) (pr1 y) (pr1 z) (pr2 w) (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