Lemma precomp_bincoprod_distributor_law : bincoprod_distributor_iso_law _ _ _ precomp_bincoprod_distributor_data. 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.
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.