proposition: Proposition eq_profunctor_nat_trans {C₁ C₂ : category} {P Q : profunctor C₁ C₂} {τ τ' : profunctor_nat_trans P Q} (p : ∏ (y : C₂) (x : C₁) (h : P y x), τ y x h = τ' y x h) : τ = τ'.
proof: Proof. use nat_trans_eq. { apply homset_property. } intros xy. induction xy as [ y x ] ; cbn. use funextsec. intro h. exact (p y x h). Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Categories.HSET.SetCoends UniMath.CategoryTheory.Profunctors.Core UniMath.CategoryTheory.Profunctors.Examples