proposition: Lemma rassociator_fun_natural {a b c d : C} : is_nat_trans (precategory_binproduct_assoc (hom a b) (hom b c) (hom c d) ∙ pair_functor hcomp_functor (functor_identity _) ∙ hcomp_functor) (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