proposition: Lemma Product_endo_is_identity (P : Product _ _ a) (k : P --> P) (H1 : ∏ i, k · ProductPr _ _ P i = ProductPr _ _ P i) : identity _ = k.
proof: Proof. apply pathsinv0. eapply pathscomp0. apply ProductArrowEta. apply pathsinv0. apply ProductArrowUnique; intro i; apply pathsinv0. now rewrite id_left, H1. 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