Proposition rmap_comp_profunctor {z : C₃} {x₁ x₂ : C₁} (f : x₁ --> x₂) {y : C₂} (h : P y x₁) (h' : Q z y) : rmap comp_profunctor f (comp_profunctor_ob_in y h h') = comp_profunctor_ob_in y (rmap P f h) h'. Proof. cbn. rewrite comp_profunctor_mor_comm. 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.