Definition PS_disp_tensor_data : disp_bifunctor_data SET_cartesian_monoidal DPS DPS DPS. Proof. repeat (use tpair). - exact (λ _ _ x y, x,,y). - intros X Y Z f x y z pf. use total2_paths_b. + apply idpath. + cbn in *. apply pf. - intros X Y1 Y2 g x y1 y2 pg. 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.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.Structure.Cartesian. Require Import UniMath.CategoryTheory.Monoidal.Examples.DisplayedCartesianMonoidal. Require Import UniMath.CategoryTheory.Monoidal.Examples.CartesianMonoidal. Import DisplayedBifunctorNotations.