Lemma BinCoproductIn1Commutes_left_in_ctx (f : a --> c)(g : b --> c)(h : c --> d)(h' : a --> d): BinCoproductIn1 C (CC _ _) · (BinCoproductArrow C (CC _ _) f g · h) = h' -> f · h = h'. Proof. intro Hyp. rewrite assoc in Hyp. rewrite BinCoproductIn1Commutes in Hyp. exact Hyp. 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.