Lemma is_nat_trans_coproduct_nat_trans_in2_data : is_nat_trans _ _ coproduct_nat_trans_in2_data. Proof. unfold is_nat_trans. intros c c' f. unfold coproduct_nat_trans_in2_data. unfold BinCoproduct_of_functors. simpl. unfold BinCoproduct_of_functors_mor. assert (XX:= BinCoproductOfArrowsIn2). assert (X1 := XX _ (F c) (G c) (HD (F c) (G c))). assert (X2 := X1 _ _ (HD (F c') (G c'))). rewrite X2. 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.