-- Lean 4 proof step from Mathlib.Algebra.Homology.BifunctorShift (goal)
Goal:
C₁ : Type u_1
C₂ : Type u_2
D : Type u_3
inst : Category.{v_1, u_1} C₁
inst_1 : Category.{v_2, u_2} C₂
inst_2 : Category.{v_3, u_3} D
inst_3 : HasZeroMorphisms.{v_1, u_1} C₁
inst_4 : Preadditive.{v_2, u_2} C₂
inst_5 : Preadditive.{v_3, u_3} D
K₁ : CochainComplex.{v_1, u_1, 0} C₁ ℤ
K₂ L₂ : CochainComplex.{v_2, u_2, 0} C₂ ℤ
f₂ : K₂ ⟶ L₂
F : C₁ ⥤ CategoryTheory.Functor.{v_2, v_3, u_2, u_3} C₂ D
inst_6 : F.PreservesZeroMorphisms
inst_7 : ∀ (X₁ : C₁), (F.obj X₁).Additive
y : ℤ
inst_8 : K₁.HasMapBifunctor K₂ F
i j : ℤ
h : (ComplexShape.up ℤ).Rel i j
i_1 : ℤ
⊢ Eq (α :=
    X
        (X
          (Functor.obj (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
            (Functor.obj (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y) K₂))
          i)
        i_1 ⟶
      X
        (X
          (Functor.obj (HomologicalComplex₂.shiftFunctor₂ D y)
            (Functor.obj (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
              K₂))
          j)
        i_1)
    (Hom.f
      (Iso.hom
          ((fun (i₁ : ℤ) ↦
              (Hom.isoOfComponents
                  (fun (x : ℤ) ↦
                    Iso.refl
                      (X
                        (X
                          (Functor.obj
                            (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
                            (Functor.obj
                              (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y)
                              K₂))
                          i₁)
                        x))
                  ⋯ :
                Iso (C := HomologicalComplex.{v_3, u_3, 0} D (ComplexShape.up ℤ))
                  (X
                    (Functor.obj
                      (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
                      (Functor.obj
                        (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y) K₂))
                    i₁)
                  (X
                    (Functor.obj (HomologicalComplex₂.shiftFunctor₂ D y)
                      (Functor.obj
                        (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁) K₂))
                    i₁)))
            i) ≫
        d
          (Functor.obj (HomologicalComplex₂.shiftFunctor₂ D y)
            (Functor.obj (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
              K₂))
          i j)
      i_1)
    (Hom.f
      (d
          (Functor.obj (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
            (Functor.obj (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y) K₂))
          i j ≫
        Iso.hom
          ((fun (i₁ : ℤ) ↦
              (Hom.isoOfComponents
                  (fun (x : ℤ) ↦
                    Iso.refl
                      (X
                        (X
                          (Functor.obj
                            (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
                            (Functor.obj
                              (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y)
                              K₂))
                          i₁)
                        x))
                  ⋯ :
                Iso (C := HomologicalComplex.{v_3, u_3, 0} D (ComplexShape.up ℤ))
                  (X
                    (Functor.obj
                      (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁)
                      (Functor.obj
                        (CategoryTheory.shiftFunctor (HomologicalComplex.{v_2, u_2, 0} C₂ (ComplexShape.up ℤ)) y) K₂))
                    i₁)
                  (X
                    (Functor.obj (HomologicalComplex₂.shiftFunctor₂ D y)
                      (Functor.obj
                        (Functor.obj (F.mapBifunctorHomologicalComplex (ComplexShape.up ℤ) (ComplexShape.up ℤ)) K₁) K₂))
                    i₁)))
            j))
      i_1)
have h : 𝟙 ((F.obj (K₁.X i)).obj (K₂.X (i_1 + y))) ≫ (F.map (K₁.d i j)).app (K₂.X (i_1 + y)) =
  (F.map (K₁.d i j)).app (K₂.X (i_1 + y)) ≫ 𝟙 ((F.obj (K₁.X j)).obj (K₂.X (i_1 + y)))
Tactic: dsimp