proposition: Lemma ProductPrCommutes (c : ∏ i, C) (P : Product c) : ∏ (a : C) (f : ∏ i, a --> c i) i, ProductArrow P f · ProductPr P i = f i.
proof: Proof. intros a f i. apply (pr2 (pr1 (isProduct_Product P _ f)) 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