Definition BO_disp_tensor_data : disp_bifunctor_data SET_cartesian_monoidal DBO DBO DBO. Proof. repeat (use tpair). - intros X Y m n. intros xy1 xy2. exact (m (pr1 xy1) (pr1 xy2),, n (pr2 xy1) (pr2 xy2)). - intros X Y Z f m n o pf. intros x1 x2. use total2_paths_b. + apply idpath. + cbn in *. apply pf. - intros X Y1 Y2 g m m1 m2 pg. intros xy1 xy2. use total2_paths_b. + cbn in *; apply pg. + cbn in *. unfold transportb. rewrite transportf_const. apply idpath. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.WhiskeredDisplayedBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Displayed.Monoidal. Require Import UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.DisplayedCartesianMonoidal.