Proposition enriched_relation_rassociator {W X Y Z : hSet} (R₁ : enriched_relation V W X) (R₂ : enriched_relation V X Y) (R₃ : enriched_relation V Y Z) : enriched_relation_square (idfun _) (idfun _) (R₁ ·e (R₂ ·e R₃)) ((R₁ ·e R₂) ·e R₃). Proof. intros w z ; cbn. use CoproductArrow. intro x. use arrow_from_tensor_coproduct_benabou_cosmos. intro y ; cbn. refine (mon_rassociator _ _ _ · _). refine ((_ #⊗ identity _)· CoproductIn _ _ _ y). exact (CoproductIn _ _ _ x). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.PosetCat. Require Import UniMath.CategoryTheory.Limits.Coends. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.Limits.Preservation. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.