Proposition enriched_relation_lunitor {X Y : hSet} (R : enriched_relation V X Y) : enriched_relation_square (idfun _) (idfun _) (id_enriched_relation _ ·e R) R. Proof. intros x y ; cbn. use CoproductArrow. intro y' ; cbn. refine (sym_mon_braiding _ _ _ · _). use arrow_from_tensor_coproduct_benabou_cosmos. intro p ; cbn. induction p. apply mon_runitor. 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.