proposition: Lemma BinProduct_endo_is_identity (P : BinProduct _ a b) (k : BinProductObject _ P --> BinProductObject _ P) (H1 : k · BinProductPr1 _ P = BinProductPr1 _ P) (H2 : k · BinProductPr2 _ P = BinProductPr2 _ P) : identity _ = k.
proof: Proof. apply pathsinv0. eapply pathscomp0. apply BinProductArrowEta. apply pathsinv0. apply BinProductArrowUnique; apply pathsinv0. + rewrite id_left. exact H1. + rewrite id_left. exact H2. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets