Lemma postcompWithBinProductArrow {c d : C} (Pcd : BinProductCone c d) {a b : C} (Pab : BinProductCone a b) (f : C⟦a,c⟧) (g : C⟦b,d⟧) {x : C} (k : C⟦x,a⟧) (h : C⟦x,b⟧) : BinProductArrow Pab k h · BinProductOfArrows Pcd Pab f g = BinProductArrow Pcd (k · f) (h · g). Proof. apply BinProductArrowUnique. - now rewrite <- assoc, BinProductOfArrowsPr1, assoc, BinProductPr1Commutes. - now rewrite <- assoc, BinProductOfArrowsPr2, 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.