proposition: Proposition BinProductOfArrows_swap {x₁ x₂ : C} {y₁ y₂ : C} (f : x₁ --> x₂) (g : y₁ --> y₂) : BinProductOfArrows C (prodC _ _) (prodC _ _) f g · prod_swap x₂ y₂ = prod_swap x₁ y₁ · BinProductOfArrows C _ _ g f.
proof: Proof. use BinProductArrowsEq. - unfold prod_swap. rewrite !assoc'. rewrite BinProductPr1Commutes. rewrite BinProductOfArrowsPr2. rewrite BinProductOfArrowsPr1. rewrite !assoc. rewrite BinProductPr1Commutes. apply idpath. - unfold prod_swap. rewrite !assoc'. rewrite BinProductPr2Commutes. rewrite BinProductOfArrowsPr2. rewrite BinProductOfArrowsPr1. rewrite !assoc. rewrite BinProductPr2Commutes. 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