proposition: Proposition profunctor_nat_trans_lmap_rmap {C₁ C₂ : category} {P Q : profunctor C₁ C₂} (τ : profunctor_nat_trans P Q) {y₁ y₂ : C₂} {x₁ x₂ : C₁} (g : y₂ --> y₁) (f : x₁ --> x₂) (h : P y₁ x₁) : τ y₂ x₂ (lmap P g (rmap P f h)) = lmap Q g (rmap Q f (τ y₁ x₁ h)).
proof: Proof. rewrite profunctor_nat_trans_lmap. rewrite profunctor_nat_trans_rmap. apply idpath. 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