proposition: Proposition prod_swap_swap (x y : C) : prod_swap x y · prod_swap y x = identity _.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets