Lemma precompWithBinProductArrow {c d : C} (Pcd : BinProductCone c d) {a : C} (f : C⟦a,c⟧) (g : C⟦a,d⟧) {x : C} (k : C⟦x,a⟧) : k · BinProductArrow Pcd f g = BinProductArrow Pcd (k · f) (k · g). Proof. apply BinProductArrowUnique. - now rewrite <- assoc, BinProductPr1Commutes. - now rewrite <- assoc, BinProductPr2Commutes. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits.