proposition: Lemma rassociator_fun'_natural {a b c d : C} : is_nat_trans (pair_functor hcomp_functor (functor_identity _) ∙ hcomp_functor) (precategory_binproduct_unassoc (hom a b) (hom b c) (hom c d) ∙ pair_functor (functor_identity _) hcomp_functor ∙ hcomp_functor) rassociator_fun'.
proof: 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.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.PrecategoryBinProduct