Proposition enriched_profunctor_dwhisker_square_id_comp_law : dwhisker_square_id_comp_law enriched_profunctor_ver_bicat_sq_id_comp_whisker. Proof. split. - intros C₁ C₂ C₃ C₄ F G P Q τ. use eq_enriched_profunctor_transformation ; intros z x ; cbn. rewrite enriched_from_arr_id. rewrite !assoc'. rewrite lmap_e_id. rewrite mon_linvunitor_lunitor. apply id_right. - intros C₁ C₂ C₃ C₄ F G₁ G₂ G₃ P Q τ₁ τ₂ θ. refine (_ @ dwhisker_enriched_profunctor_square_comp _ _ _). cbn. apply maponpaths_2. apply isaprop_nat_trans_enrichment. 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.