proposition: Proposition profunctor_nat_trans_lmap {C₁ C₂ : category} {P Q : profunctor C₁ C₂} (τ : profunctor_nat_trans P Q) {y₁ y₂ : C₂} {x : C₁} (g : y₂ --> y₁) (h : P y₁ x) : τ y₂ x (lmap P g h) = lmap Q g (τ y₁ x h).
proof: Proof. rewrite lmap_functor. rewrite (profunctor_nat_trans_natural τ g (identity _) h). 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