Lemma pf : g_x · i_x · f_x = g_y · i_y · f_y. Proof. use (cancel_z_iso _ _ (z_iso_inv i_z)). refine (_ @ r @ _). - rewrite ! assoc'. apply maponpaths. rewrite assoc. use z_iso_inv_to_right. exact p_xf. - rewrite ! assoc'. apply maponpaths. rewrite assoc. use z_iso_inv_on_left. exact p_yf. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.TransportMorphisms. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.Monics. Definition UnivProductFromPullback (c d a : C) (f : a --> c) (g : a --> d): exists (UnivProductFromPullback c d a f g). Definition BinProductsFromPullbacks : BinProducts C := BinProduct_Pullback.