Lemma is_nat_trans_yon_binprod_inv : is_nat_trans _ _ yon_binprod_inv_nat_trans_data. Proof. unfold yon_binprod_inv_nat_trans_data. intros Z W f. use funextfun; intros [g1 g2]; cbn. use BinProductArrowsEq; rewrite <- assoc. - now rewrite !BinProductPr1Commutes. - now rewrite !BinProductPr2Commutes. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.Presheaf. Require Import UniMath.CategoryTheory.opp_precat. Require Import UniMath.CategoryTheory.Categories.HSET.Core. Require Import UniMath.CategoryTheory.yoneda.