Proposition enriched_profunctor_associator_cylinder_law : associator_cylinder_law enriched_profunctor_ver_bicat_sq_id_comp_whisker. Proof. split. - intros C₁ C₂ C₃ C₄ D₁ D₂ D₃ D₄ F₁ F₂ F₃ G₁ G₂ G₃ P₁ P₂ P₃ P₄ τ₁ τ₂ τ₃. pose (dwhisker_rassociator_enriched_profunctor τ₁ τ₂ τ₃ (disp_rassociator (pr2 G₁) (pr2 G₂) (pr2 G₃)) (disp_rassociator (pr2 F₁) (pr2 F₂) (pr2 F₃))) as p. refine (_ @ p @ _). + use eq_enriched_profunctor_transformation. intros x y. apply idpath. + use eq_enriched_profunctor_transformation. intros x y. apply idpath. - intros C₁ C₂ C₃ C₄ C₅ C₆ C₇ C₈ F₁ F₂ F₃ F₄ P₁ P₂ P₃ Q₁ Q₂ Q₃ τ₁ τ₂ τ₃. apply lwhisker_lassociator_enriched_profunctor. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. 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. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.RepresentableLaws. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Require Import UniMath.Bicategories.Core.Bicat. Import Bicat.Notations. Require Import UniMath.Bicategories.Core.Invertible_2cells. Require Import UniMath.Bicategories.Core.Univalence. Require Import UniMath.Bicategories.Core.UnivalenceOp. Require Import UniMath.Bicategories.Core.Examples.OpCellBicat. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.EnrichedCats. Require Import UniMath.Bicategories.DoubleCategories.DoubleBicat.Core. Import MonoidalNotations.