Proposition dwhisker_linvunitor_enriched_profunctor {V : benabou_cosmos} {C₁ C₂ C₃ C₄ : category} {E₁ : enrichment C₁ V} {E₂ : enrichment C₂ V} {E₃ : enrichment C₃ V} {E₄ : enrichment C₄ V} {F : C₁ ⟶ C₂} {EF : functor_enrichment F E₁ E₂} {G : C₃ ⟶ C₄} {EG : functor_enrichment G E₃ E₄} {P : E₁ ↛e E₃} {Q : E₂ ↛e E₄} (τ : enriched_profunctor_square EF EG P Q) (H₁ : nat_trans_enrichment (nat_trans_id _) EG (functor_comp_enrichment (functor_id_enrichment _) EG)) (H₂ : nat_trans_enrichment (nat_trans_id _) EF (functor_comp_enrichment (functor_id_enrichment _) EF)) : dwhisker_enriched_profunctor_square H₁ (comp_h_enriched_profunctor_square (id_h_enriched_profunctor_square P) τ) = uwhisker_enriched_profunctor_square H₂ τ. Proof. use eq_enriched_profunctor_transformation ; intros z x ; cbn. rewrite id_left. 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.