Proposition dwhisker_rassociator_enriched_profunctor {V : benabou_cosmos} {C₁ C₂ C₃ C₄ C₅ C₆ C₇ C₈ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} {E₄ : enrichment C₄ V} {E₅ : enrichment C₅ V} {E₆ : enrichment C₆ V} {E₇ : enrichment C₇ V} {E₈ : enrichment C₈ V} {F₁ : C₁ ⟶ C₂} {EF₁ : functor_enrichment F₁ E₁ E₂} {F₂ : C₂ ⟶ C₃} {EF₂ : functor_enrichment F₂ E₂ E₃} {F₃ : C₃ ⟶ C₄} {EF₃ : functor_enrichment F₃ E₃ E₄} {G₁ : C₅ ⟶ C₆} {EG₁ : functor_enrichment G₁ E₅ E₆} {G₂ : C₆ ⟶ C₇} {EG₂ : functor_enrichment G₂ E₆ E₇} {G₃ : C₇ ⟶ C₈} {EG₃ : functor_enrichment G₃ E₇ E₈} {P₁ : E₁ ↛e E₅} {P₂ : E₂ ↛e E₆} {P₃ : E₃ ↛e E₇} {P₄ : E₄ ↛e E₈} (τ₁ : enriched_profunctor_square EF₁ EG₁ P₁ P₂) (τ₂ : enriched_profunctor_square EF₂ EG₂ P₂ P₃) (τ₃ : enriched_profunctor_square EF₃ EG₃ P₃ P₄) (H₁ : nat_trans_enrichment (nat_trans_id _) (functor_comp_enrichment (functor_comp_enrichment EG₁ EG₂) EG₃) (functor_comp_enrichment EG₁ (functor_comp_enrichment EG₂ EG₃))) (H₂ : nat_trans_enrichment (nat_trans_id _) (functor_comp_enrichment (functor_comp_enrichment EF₁ EF₂) EF₃) (functor_comp_enrichment EF₁ (functor_comp_enrichment EF₂ EF₃))) : dwhisker_enriched_profunctor_square H₁ (comp_h_enriched_profunctor_square τ₁ (comp_h_enriched_profunctor_square τ₂ τ₃)) = uwhisker_enriched_profunctor_square H₂ (comp_h_enriched_profunctor_square (comp_h_enriched_profunctor_square τ₁ τ₂) τ₃). Proof. use eq_enriched_profunctor_transformation ; intros z x ; cbn. rewrite !assoc'. rewrite !enriched_from_arr_id. rewrite lmap_e_id, rmap_e_id. apply idpath. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.whiskering. 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.