Definition comp_v_enriched_profunctor_square_mor : enriched_profunctor_transformation_data (comp_enriched_profunctor P₁ P₂) (precomp_enriched_profunctor EF₁ EF₃ (comp_enriched_profunctor Q₁ Q₂)). Proof. intros z x ; cbn. use from_comp_enriched_profunctor_ob. - exact (λ y, (τ y x #⊗ θ z y) · comp_enriched_profunctor_in _ _ (F₃ z) (F₁ x) (F₂ y)). - intros y₁ y₂ ; cbn. exact (comp_v_enriched_profunctor_square_mor_eq z y₁ y₂ x). Defined.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.EnrichedCats.BenabouCosmos. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentTransformation. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.StandardProfunctors. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorTransformations. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Invertible. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.ProfunctorSquares. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Coend. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Composition.CompositionProf. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.