Proposition eq_enriched_relation {V : quantale_cosmos} {X Y : hSet} {R R' : enriched_relation V X Y} (p : ∏ (x : X) (y : Y), R x y --> R' x y) (q : ∏ (x : X) (y : Y), R' x y --> R x y) : R = R'. Proof. use funextsec ; intro x. use funextsec ; intro y. use isotoid. { apply is_univalent_quantale_cosmos. } use make_z_iso. - exact (p x y). - exact (q x y). - split ; apply is_poset_category_quantale_cosmos. 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.