Lemma rassociator_fun'_natural {a b c d : C} : is_nat_trans (pair_functor hcomp_functor (functor_identity _) ∙ hcomp_functor) (precategory_binproduct_unassoc (hom_precategory a b) (hom_precategory b c) (hom_precategory c d) ∙ pair_functor (functor_identity _) hcomp_functor ∙ hcomp_functor) rassociator_fun'. Proof. red; cbn. intros ((f1, f2), f3) ((g1, g2), g3). unfold precategory_binproduct_mor, hom_ob_mor. cbn. unfold precategory_binproduct_mor, hom_ob_mor. cbn. intros ((x1, x2), x3). cbn. unfold rassociator_fun. cbn. apply hcomp_rassoc. 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.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.PrecategoryBinProduct.