Lemma BinCoproductIn2Commutes_right_in_double_ctx (g0 : x --> b)(f : a --> c)(g : b --> c) (h : c --> d)(h' : x --> d): h' = g0 · BinCoproductIn2 C (CC _ _) · (BinCoproductArrow C (CC _ _) f g · h) -> h' = g0 · g · h. Proof. intro Hyp. rewrite Hyp. repeat rewrite <- assoc. apply maponpaths. rewrite assoc. rewrite 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.