proposition: Lemma ProductOfArrowsPr {c : ∏ i, C} (Pc : Product c) {a : ∏ i, C} (Pa : Product a) (f : ∏ i, a i --> c i) : ∏ i, ProductOfArrows Pc Pa f · ProductPr Pc i = ProductPr Pa i · f i.
proof: Proof. unfold ProductOfArrows; intro i. now rewrite (ProductPrCommutes _ _ _ _ i). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.ProductCategory UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.Combinatorics.StandardFiniteSets