Proposition identity_enriched_profunctor_lmap_e_arr (y : C) {x₁ x₂ : C} (g : x₁ --> x₂) : lmap_e_arr identity_enriched_profunctor y g = precomp_arr E y g. Proof. unfold lmap_e_arr ; cbn. rewrite !assoc. etrans. { apply maponpaths_2. rewrite !assoc'. rewrite tensor_sym_mon_braiding. rewrite !assoc. rewrite sym_mon_braiding_linvunitor. apply idpath. } apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.EnrichedCats.Enrichment. Require Import UniMath.CategoryTheory.EnrichedCats.EnrichmentFunctor. Require Import UniMath.CategoryTheory.EnrichedCats.Profunctors.Profunctor. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Structure.Symmetric. Require Import UniMath.CategoryTheory.Monoidal.Structure.Closed. Import MonoidalNotations.