Proposition lwhisker_uwhisker_enriched_profunctor_square {V : benabou_cosmos} {C₁ C₂ C₃ C₄ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} {E₄ : enrichment C₄ V} {F₁ F₂ : C₁ ⟶ C₂} {EF₁ : functor_enrichment F₁ E₁ E₂} {EF₂ : functor_enrichment F₂ E₁ E₂} {τ₁ : F₁ ⟹ F₂} (Hτ₁ : nat_trans_enrichment τ₁ EF₁ EF₂) {G : C₃ ⟶ C₄} {EG : functor_enrichment G E₃ E₄} {P₁ P₂ : E₁ ↛e E₃} (τ₂ : enriched_profunctor_transformation P₁ P₂) {Q : E₂ ↛e E₄} (θ : enriched_profunctor_square EF₁ EG P₂ Q) : lwhisker_enriched_profunctor_square τ₂ (uwhisker_enriched_profunctor_square Hτ₁ θ) = uwhisker_enriched_profunctor_square Hτ₁ (lwhisker_enriched_profunctor_square τ₂ θ). Proof. use eq_enriched_profunctor_transformation ; intros z x ; cbn. rewrite !assoc'. apply idpath. Qed.
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.EnrichedCats.Profunctors.Composition.SquareComp. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Composition.Unitors. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Composition.Associators. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Composition.Whiskering. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.