Proposition prod_profunctor_laws : profunctor_laws prod_profunctor_data. Proof. repeat split ; cbn. - intros y x h. rewrite !profunctor_id. apply idpath. - intros y₁ y₂ y₃ g₁ g₂ x₁ x₂ x₃ f₁ f₂ h. rewrite !profunctor_comp. apply idpath. - intros y x. apply isaset_dirprod ; apply setproperty. 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.