Proposition lax_extension_enriched_rel_comp {V : quantale_cosmos} {F : SET ⟶ SET} (L : lax_extension V F) {X Y Z : hSet} (R : enriched_relation V X Y) (S : enriched_relation V Y Z) : L _ _ R ·e L _ _ S ≤e L _ _ (R ·e S). Proof. exact (pr122 L X Y Z R S). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichedRelation. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.CategoryTheory.Limits.Coproducts. Import MonoidalNotations.