proposition: Lemma precompWithProductArrow {c : ∏ i, C} (Pc : Product c) {a : C} (f : ∏ i, a --> c i) {x : C} (k : x --> a) : k · ProductArrow Pc f = ProductArrow Pc (λ i, k · f i).
proof: Proof. apply ProductArrowUnique; intro i. now rewrite <- assoc, ProductPrCommutes. 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