proposition: Lemma precomp_bincoprod_distributor_law : bincoprod_distributor_iso_law _ _ _ precomp_bincoprod_distributor_data.
proof: Proof. intros F G. split. - apply (nat_trans_eq C). intro c. cbn. rewrite id_left. apply pathsinv0, BinCoproduct_endo_is_identity. + apply BinCoproductIn1Commutes. + apply BinCoproductIn2Commutes. - etrans. { apply postcompWithBinCoproductArrow. } etrans. 2: { apply pathsinv0, BinCoproductArrowEta. } apply maponpaths_12; (rewrite id_right; apply (nat_trans_eq C); intro c; apply id_right). 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