proposition: Lemma precompWithBinProductArrow {c d : C} (Pcd : BinProduct c d) {a : C} (f : a --> c) (g : a --> d) {x : C} (k : x --> a) : k · BinProductArrow Pcd f g = BinProductArrow Pcd (k · f) (k · g).
proof: Proof. apply BinProductArrowUnique. - rewrite <- assoc, BinProductPr1Commutes; apply idpath. - rewrite <- assoc, BinProductPr2Commutes; apply idpath. 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