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