-- Module: Mathlib.Algebra.Homology.BifunctorAssociator
Goal:
C₁ : Type u_1
C₂ : Type u_2
C₂₃ : Type u_4
C₃ : Type u_5
C₄ : Type u_6
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_5} C₃
inst_3 : Category.{v_4, u_6} C₄
inst_4 : Category.{v_6, u_4} C₂₃
inst_5 : HasZeroMorphisms.{v_1, u_1} C₁
inst_6 : HasZeroMorphisms.{v_2, u_2} C₂
inst_7 : HasZeroMorphisms.{v_3, u_5} C₃
inst_8 : Preadditive.{v_6, u_4} C₂₃
inst_9 : Preadditive.{v_4, u_6} C₄
F : C₁ ⥤ CategoryTheory.Functor.{v_6, v_4, u_4, u_6} C₂₃ C₄
G₂₃ : C₂ ⥤ CategoryTheory.Functor.{v_3, v_6, u_5, u_4} C₃ C₂₃
inst_10 : G₂₃.PreservesZeroMorphisms
inst_11 : ∀ (X₂ : C₂), (G₂₃.obj X₂).PreservesZeroMorphisms
inst_12 : F.PreservesZeroMorphisms
inst_13 : ∀ (X₁ : C₁), (F.obj X₁).Additive
ι₁ : Type u_7
ι₂ : Type u_8
ι₃ : Type u_9
ι₁₂ : Type u_10
ι₂₃ : Type u_11
ι₄ : Type u_12
inst_14 : DecidableEq ι₄
c₁ : ComplexShape ι₁
c₂ : ComplexShape ι₂
c₃ : ComplexShape ι₃
K₁ : HomologicalComplex.{v_1, u_1, u_7} C₁ c₁
K₂ : HomologicalComplex.{v_2, u_2, u_8} C₂ c₂
K₃ : HomologicalComplex.{v_3, u_5, u_9} C₃ c₃
c₁₂ : ComplexShape ι₁₂
c₂₃ : ComplexShape ι₂₃
c₄ : ComplexShape ι₄
inst_15 : TotalComplexShape c₁ c₂ c₁₂
inst_16 : TotalComplexShape c₁₂ c₃ c₄
inst_17 : TotalComplexShape c₂ c₃ c₂₃
inst_18 : TotalComplexShape c₁ c₂₃ c₄
inst_19 : K₂.HasMapBifunctor K₃ G₂₃ c₂₃
inst_20 : c₁.Associative c₂ c₃ c₁₂ c₂₃ c₄
inst_21 : DecidableEq ι₂₃
inst_22 : K₁.HasMapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄
inst_23 : HasGoodTrifunctor₂₃Obj F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄
j j' : ι₄
e_a :
  ∀ (i₁ : ι₁) (i₂ : ι₂) (i₃ : ι₃) (h : c₁.r c₂ c₃ c₁₂ c₄ (i₁, i₂, i₃) = j),
    CategoryStruct.comp (Y := X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
        (ι F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j h :
          (F.obj (K₁.X i₁)).obj ((G₂₃.obj (K₂.X i₂)).obj (K₃.X i₃)) ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j)
        (mapBifunctor.D₂ K₁ (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄ j j' :
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j') =
      ι F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ i₁ i₂ i₃ j h ≫
        HAdd.hAdd (α :=
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
          (β :=
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
          (D₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ j j' :
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
              X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
          (D₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ j j' :
            X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
              X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
⊢ mapBifunctor.D₂ K₁ (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄ j j' =
    HAdd.hAdd (α :=
      X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
      (β :=
      X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
      (D₂ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ j j' :
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')
      (D₃ F G₂₃ K₁ K₂ K₃ c₁₂ c₂₃ c₄ j j' :
        X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j ⟶
          X (K₁.mapBifunctor (K₂.mapBifunctor K₃ G₂₃ c₂₃) F c₄) j')

Tactic:
apply mapBifunctor₂₃.hom_ext (c₁₂ := c₁₂)

Premises used: HomologicalComplex.mapBifunctor₂₃.hom_ext