proposition: Proposition profunctor_square_lmap_rmap {C₁ C₂ D₁ D₂ : category} {F : C₁ ⟶ C₂} {G : D₁ ⟶ D₂} {P : D₁ ↛ C₁} {Q : D₂ ↛ C₂} (τ : profunctor_square F G P Q) {y₁ y₂ : C₁} {x₁ x₂ : D₁} (g : y₂ --> y₁) (f : x₁ --> x₂) (h : P y₁ x₁) : τ y₂ x₂ (lmap P g (rmap P f h)) = lmap Q (#F g) (rmap Q (#G f) (τ y₁ x₁ h)).
proof: Proof. rewrite (profunctor_square_lmap τ g). apply maponpaths. apply profunctor_square_rmap. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Categories.HSET.All UniMath.CategoryTheory.Categories.HSET.SetCoends UniMath.CategoryTheory.Profunctors.Core UniMath.CategoryTheory.Profunctors.Examples UniMath.CategoryTheory.Profunctors.Transformation