-- CategoryTheory.GradedObject.mapBifunctor_triangle
lemma mapBifunctor_triangle :
    (mapBifunctorAssociator associator τ.ρ₁₂ τ.ρ₂₃ X₁ ((single₀ I₂).obj X₂) X₃).hom ≫
    mapBifunctorMapMap G π (𝟙 X₁) (mapBifunctorLeftUnitor F₂ X₂ e₂ τ.p₂₃ τ.h₃ X₃).hom =
      mapBifunctorMapMap G π (mapBifunctorRightUnitor F₁ X₂ e₁ τ.p₁₂ τ.h₁ X₁).hom (𝟙 X₃) 
Arguments: {C₁ : Type u_1} {C₂ : Type u_2} {C₃ : Type u_3} {D : Type u_4} {I₁ : Type u_5} {I₂ : Type u_6} {I₃ : Type u_7} {J : Type u_8} [CategoryTheory.Category.{u_10, u_1} C₁] [CategoryTheory.Category.{u_12, u_2} C₂] [CategoryTheory.Category.{u_11, u_3} C₃] [CategoryTheory.Category.{u_9, u_4} D] [Zero I₂] [DecidableEq I₂] [CategoryTheory.Limits.HasInitial C₂] {F₁ : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ C₁)} {F₂ : CategoryTheory.Functor C₂ (CategoryTheory.Functor C₃ C₃)} {G : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₃ D)} (associator : CategoryTheory.bifunctorComp₁₂ F₁ G ≅ CategoryTheory.bifunctorComp₂₃ G F₂) (X₂ : C₂) (e₁ : F₁.flip.obj X₂ ≅ CategoryTheory.Functor.id C₁) (e₂ : F₂.obj X₂ ≅ CategoryTheory.Functor.id C₃) [(X₁ : C₁) → CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C₂) (F₁.obj X₁)] [(X₃ : C₃) → CategoryTheory.Limits.PreservesColimit (CategoryTheory.Functor.empty C₂) (F₂.flip.obj X₃)] {r : I₁ × I₂ × I₃ → J} {π : I₁ × I₃ → J} (τ : CategoryTheory.GradedObject.TriangleIndexData r π) (X₁ : CategoryTheory.GradedObject I₁ C₁) (X₃ : CategoryTheory.GradedObject I₃ C₃) [(((CategoryTheory.GradedObject.mapBifunctor F₁ I₁ I₂).obj X₁).obj
        ((CategoryTheory.GradedObject.single₀ I₂).obj X₂)).HasMap
    τ.p₁₂] [(((CategoryTheory.GradedObject.mapBifunctor G I₁ I₃).obj
            (CategoryTheory.GradedObject.mapBifunctorMapObj F₁ τ.p₁₂ X₁
              ((CategoryTheory.GradedObject.single₀ I₂).obj X₂))).obj
        X₃).HasMap
    π] [(((CategoryTheory.GradedObject.mapBifunctor F₂ I₂ I₃).obj ((CategoryTheory.GradedObject.single₀ I₂).obj X₂)).obj
        X₃).HasMap
    τ.p₂₃] [(((CategoryTheory.GradedObject.mapBifunctor G I₁ I₃).obj X₁).obj
        (CategoryTheory.GradedObject.mapBifunctorMapObj F₂ τ.p₂₃ ((CategoryTheory.GradedObject.single₀ I₂).obj X₂)
          X₃)).HasMap
    π] [CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj F₁ G τ.ρ₁₂ X₁ ((CategoryTheory.GradedObject.single₀ I₂).obj X₂) X₃] [CategoryTheory.GradedObject.HasGoodTrifunctor₂₃Obj G F₂ τ.ρ₂₃ X₁ ((CategoryTheory.GradedObject.single₀ I₂).obj X₂) X₃] [(((CategoryTheory.GradedObject.mapBifunctor G I₁ I₃).obj X₁).obj X₃).HasMap π] (triangle :
  ∀ (X₁ : C₁) (X₃ : C₃),
    CategoryTheory.CategoryStruct.comp (((associator.hom.app X₁).app X₂).app X₃) ((G.obj X₁).map (e₂.hom.app X₃)) =
      (G.map (e₁.hom.app X₁)).app X₃)
Goal: CategoryTheory.CategoryStruct.comp
    (CategoryTheory.GradedObject.mapBifunctorAssociator associator τ.ρ₁₂ τ.ρ₂₃ X₁
        ((CategoryTheory.GradedObject.single₀ I₂).obj X₂) X₃).hom
    (CategoryTheory.GradedObject.mapBifunctorMapMap G π (CategoryTheory.CategoryStruct.id X₁)
      (CategoryTheory.GradedObject.mapBifunctorLeftUnitor F₂ X₂ e₂ τ.p₂₃ ⋯ X₃).hom) =
  CategoryTheory.GradedObject.mapBifunctorMapMap G π
    (CategoryTheory.GradedObject.mapBifunctorRightUnitor F₁ X₂ e₁ τ.p₁₂ ⋯ X₁).hom (CategoryTheory.CategoryStruct.id X₃)