Lemma precompWithBinCoproductArrow_eq (CCab : BinCoproduct a b) (CCcd : BinCoproduct c d) (f : a --> c) (g : b --> d) (k : c --> x) (h : d --> x) (fk : a --> x) (gh : b --> x): fk = f · k → gh = g · h → BinCoproductOfArrows _ CCab CCcd f g · BinCoproductArrow CCcd k h = BinCoproductArrow CCab (fk) (gh). Proof. intros H H'. rewrite H. rewrite H'. apply precompWithBinCoproductArrow. 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.