Proposition rmap_precomp_profunctor {x₁ x₂ : C₁} {y : D₁} (f : x₁ --> x₂) (h : P (G y) (F x₁)) : rmap precomp_profunctor f h = rmap P (#F f) h. Proof. cbn. rewrite functor_id. rewrite lmap_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.