Proposition enriched_relation_lassociator {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 y ; cbn. refine (sym_mon_braiding _ _ _ · _). use arrow_from_tensor_coproduct_benabou_cosmos. intro x ; cbn. refine (sym_mon_braiding _ _ _ · _). refine (mon_lassociator _ _ _ · _). refine ((identity _ #⊗ _)· CoproductIn _ _ _ x). exact (CoproductIn _ _ _ y). 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.