Definition Binop_dispBinproducts : dispBinProducts Binop_disp_cat BinProductsHSET. Proof. intros X Y m n. use make_dispBinProduct_locally_prop. - exact Binop_disp_cat_locally_prop. - use tpair. + intros xy1 xy2. exact (m (pr1 xy1) (pr1 xy2),, n (pr2 xy1) (pr2 xy2)). + split; intros x1 x2; apply idpath. - intros Z f g o pf pg. cbn. intros x1 x2. apply dirprodeq; cbn. + rewrite pf. apply idpath. + rewrite pg. 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.