proposition: Lemma is_nat_trans_coproduct_nat_trans_in2_data : is_nat_trans _ _ coproduct_nat_trans_in2_data.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory