Definition enriched_profunctor_ver_sq_bicat_id_comp_cells : ver_sq_bicat_id_comp_cells enriched_profunctor_ver_sq_bicat_ver_id_comp. Proof. repeat split. - exact (λ (C₁ C₂ : enriched_cat V) (P : C₁ ↛e C₂), enriched_profunctor_id_transformation P). - exact (λ (C₁ C₂ : enriched_cat V) (P : C₁ ↛e C₂), lunitor_enriched_profunctor P). - exact (λ (C₁ C₂ : enriched_cat V) (P : C₁ ↛e C₂), runitor_enriched_profunctor P). - exact (λ (C₁ C₂ : enriched_cat V) (P : C₁ ↛e C₂), linvunitor_enriched_profunctor P). - exact (λ (C₁ C₂ : enriched_cat V) (P : C₁ ↛e C₂), rinvunitor_enriched_profunctor P). - exact (λ (C₁ C₂ C₃ C₄ : enriched_cat V) (P : C₁ ↛e C₂) (Q : C₂ ↛e C₃) (R : C₃ ↛e C₄), rassociator_enriched_profunctor P Q R). - exact (λ (C₁ C₂ C₃ C₄ : enriched_cat V) (P : C₁ ↛e C₂) (Q : C₂ ↛e C₃) (R : C₃ ↛e C₄), lassociator_enriched_profunctor P Q R). - exact (λ (C₁ C₂ : enriched_cat V) (P Q R : C₁ ↛e C₂) (τ : enriched_profunctor_transformation P Q) (θ : enriched_profunctor_transformation Q R), enriched_profunctor_comp_transformation τ θ). - exact (λ (C₁ C₂ C₃ : enriched_cat V) (P : C₁ ↛e C₂) (Q₁ Q₂ : C₂ ↛e C₃) (τ : enriched_profunctor_transformation Q₁ Q₂), lwhisker_enriched_profunctor P τ). - exact (λ (C₁ C₂ C₃ : enriched_cat V) (P₁ P₂ : C₁ ↛e C₂) (Q : C₂ ↛e C₃) (τ : enriched_profunctor_transformation P₁ P₂), rwhisker_enriched_profunctor τ Q). Defined.
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.