Proposition lmap_id_profunctor {x y₁ y₂ : C} (f : y₂ --> y₁) (h : y₁ --> x) : lmap id_profunctor f h = f · h. Proof. cbn. rewrite id_right. apply idpath. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Categories.HSET.All. Require Import UniMath.CategoryTheory.Categories.HSET.SetCoends. Require Import UniMath.CategoryTheory.Profunctors.Core.