Proposition prod_swap_swap (x y : C) : prod_swap x y · prod_swap y x = identity _. Proof. use BinProductArrowsEq. - unfold prod_swap. rewrite !assoc'. rewrite !id_left. rewrite BinProductPr1Commutes. rewrite BinProductPr2Commutes. apply idpath. - unfold prod_swap. rewrite !assoc'. rewrite !id_left. rewrite BinProductPr2Commutes. rewrite BinProductPr1Commutes. apply idpath. 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.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits. Require Import UniMath.CategoryTheory.Limits.Products. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.Combinatorics.StandardFiniteSets. Section BinProductFromIso. End BinProductFromIso. Section BinProductsFromProducts. End BinProductsFromProducts. Section ProductsFromBinProducts. End ProductsFromBinProducts.