proposition: Lemma postcompWithBinProductArrow {c d : C} (Pcd : BinProduct c d) {a b : C} (Pab : BinProduct a b) (f : a --> c) (g : b --> d) {x : C} (k : x --> a) (h : x --> b) : BinProductArrow Pab k h · BinProductOfArrows Pcd Pab f g = BinProductArrow Pcd (k · f) (h · g).
proof: Proof. apply BinProductArrowUnique. - rewrite <- assoc, BinProductOfArrowsPr1. rewrite assoc, BinProductPr1Commutes. apply idpath. - rewrite <- assoc, BinProductOfArrowsPr2. 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