proposition: Lemma total_functoronmorphisms_are_equal {C : category} {D : disp_cat C} {M : monoidal C} (DT : disp_tensor D M) : functoronmorphisms_are_equal (total_tensor_data DT).
proof: Proof. intros x1 x2 y1 y2 f g. use total2_paths_b. - exact (bifunctor_equalwhiskers (monoidal_tensor M) (pr1 x1) (pr1 x2) (pr1 y1) (pr1 y2) (pr1 f) (pr1 g)). - exact (disp_bifunctor_equalwhiskers DT (pr1 x1) (pr1 x2) (pr1 y1) (pr1 y2) (pr1 f) (pr1 g) (pr2 x1) (pr2 x2) (pr2 y1) (pr2 y2) (pr2 f) (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