Proposition hset_struct_pair {W X Y : hSet} {PW : P W} {PX : P X} {PY : P Y} {f : W → X} {g : W → Y} (Mf : mor_hset_struct P PW PX f) (Mg : mor_hset_struct P PW PY g) : mor_hset_struct P PW (hset_struct_prod P PX PY) (prodtofuntoprod (f ,, g)). Proof. exact (pr2 (pr222 P) W X Y PW PX PY f g Mf Mg). Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions. Require Import UniMath.CategoryTheory.DisplayedCats.SIP. Require Import UniMath.CategoryTheory.DisplayedCats.Binproducts.