Lemma postcompWithBinCoproductArrow {a b : C} (CCab : BinCoproduct a b) {c : C} (f : a --> c) (g : b --> c) {x : C} (k : c --> x) : BinCoproductArrow CCab f g · k = BinCoproductArrow CCab (f · k) (g · k). Proof. apply BinCoproductArrowUnique. - rewrite assoc, BinCoproductIn1Commutes; apply idpath. - rewrite assoc, BinCoproductIn2Commutes; apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.ProductCategory.