-- 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 : Preadditive.{v_1, u_1} C₁
inst_4 : Preadditive.{v_2, u_2} C₂
inst_5 : Preadditive.{v_3, u_3} D
F : C₁ ⥤ Functor.{v_2, v_3, u_2, u_3} C₂ D
inst_6 : F.Additive
inst_7 : ∀ (X₁ : C₁), (F.obj X₁).Additive
inst_8 : ∀ (K₁ : CochainComplex.{v_1, u_1, 0} C₁ ℤ) (K₂ : CochainComplex.{v_2, u_2, 0} C₂ ℤ), K₁.HasMapBifunctor K₂ F
K₂ L₂ : CochainComplex.{v_2, u_2, 0} C₂ ℤ
g : K₂ ⟶ L₂
n : ℤ
K₁ : CochainComplex.{v_1, u_1, 0} C₁ ℤ
d : ℤ
⊢ Eq (α :=
    X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ)) d ⟶
      X (mapBifunctor K₁ L₂ F (ComplexShape.up ℤ)) (d + n))
    (CategoryStruct.comp (Y := X (mapBifunctor K₁ K₂ F (ComplexShape.up ℤ)) (d + n))
        (Hom.f (NatTrans.app (Iso.hom (commShiftIso (obj (Functor.flip F.map₂CochainComplex) K₂) n)) K₁) d)
        (Hom.f (mapBifunctorMap (𝟙 K₁) g F (ComplexShape.up ℤ)) (d + n)) :
      X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ)) d ⟶
        X (mapBifunctor K₁ L₂ F (ComplexShape.up ℤ)) (d + n))
    (CategoryStruct.comp (Y :=
        X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) L₂ F (ComplexShape.up ℤ)) d)
        (Hom.f
          (mapBifunctorMap (𝟙 (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁)) g F (ComplexShape.up ℤ)) d)
        (Hom.f (NatTrans.app (Iso.hom (commShiftIso (obj (Functor.flip F.map₂CochainComplex) L₂) n)) K₁) d) :
      X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ)) d ⟶
        X (mapBifunctor K₁ L₂ F (ComplexShape.up ℤ)) (d + n))
have w : ∀ (p q : ℤ) (h : (ComplexShape.up ℤ).π (ComplexShape.up ℤ) (ComplexShape.up ℤ) (p, q) = d),
  Eq (α :=
    (F.obj ((obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁).X p)).obj (K₂.X q) ⟶
      X (mapBifunctor K₁ L₂ F (ComplexShape.up ℤ)) (d + n))
    (CategoryStruct.comp (Y :=
      X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ)) d)
      (ιMapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ) p q d h)
      (CategoryStruct.comp (Y := X (mapBifunctor K₁ K₂ F (ComplexShape.up ℤ)) (d + n))
        (Hom.f (NatTrans.app (Iso.hom (commShiftIso (obj (Functor.flip F.map₂CochainComplex) K₂) n)) K₁) d)
        (Hom.f (mapBifunctorMap (𝟙 K₁) g F (ComplexShape.up ℤ)) (d + n))))
    (CategoryStruct.comp (Y :=
      X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ)) d)
      (ιMapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) K₂ F (ComplexShape.up ℤ) p q d h)
      (CategoryStruct.comp (Y :=
        X (mapBifunctor (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁) L₂ F (ComplexShape.up ℤ)) d)
        (Hom.f
          (mapBifunctorMap (𝟙 (obj (shiftFunctor (CochainComplex.{v_1, u_1, 0} C₁ ℤ) n) K₁)) g F (ComplexShape.up ℤ)) d)
        (Hom.f (NatTrans.app (Iso.hom (commShiftIso (obj (Functor.flip F.map₂CochainComplex) L₂) n)) K₁) d)))
Tactic: ext p q h