Proposition lmap_precomp_profunctor {x : C₁} {y₁ y₂ : D₁} (f : y₂ --> y₁) (h : P (G y₁) (F x)) : lmap precomp_profunctor f h = lmap P (#G f) h. Proof. cbn. rewrite functor_id. rewrite rmap_id. 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.