Lemma totalcategory_tensorfunctorcomp : tensorfunctor_comp TtD. Proof. intros x y x' y' x'' y'' f f' g g'. use total2_paths_b. + use tcomp. + use (((dtcomp (pr1 x) (pr1 y) (pr1 x') (pr1 y') (pr1 x'') (pr1 y'') (pr2 x) (pr2 y) (pr2 x') (pr2 y') (pr2 x'') (pr2 y'') (pr1 f) (pr1 g) (pr1 f') (pr1 g') (pr2 f) (pr2 g) (pr2 f') (pr2 g')))). 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.Monoidal.AlternativeDefinitions.MonoidalCategoriesCurried. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.DisplayedMonoidalCurried. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorsCurried. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Total.