proposition: Lemma ProductArrowUnique (c : ∏ i, C) (P : Product c) (x : C) (f : ∏ i, x --> c i) (k : x --> P) (Hk : ∏ i, k · ProductPr P i = f i) : k = ProductArrow P f.
proof: Proof. set (H' := pr2 (isProduct_Product P _ f) (k,,Hk)). apply (base_paths _ _ H'). 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