-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.Preadditive (goal)
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
inst_1 : Preadditive.{v_1, u_1} C
inst_2 : MonoidalCategory.{v_1, u_1} C
inst_3 : MonoidalPreadditive.{v_1, u_1} C
inst_4 : HasFiniteBiproducts.{v_1, u_1} C
J : Type
inst_5 : Fintype J
X : C
f : J → C
w :
  ∀ (j : J),
    Eq.{v_1 + 1} (α :=
      tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
      (CategoryStruct.comp (Y := biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
          (Iso.hom (leftDistributor X f) :
            tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶
              biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
          (biproduct.π (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j :
            (biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) ⟶
              tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) :
        tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
      (CategoryStruct.comp (Y := biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
          (∑ j : J,
            X ◁ biproduct.π f j ≫
              biproduct.ι.{0, v_1, u_1} (C := C) (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j)
          (biproduct.π (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j) :
        tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
w₁ :
  ∀ (j : J),
    Eq.{v_1 + 1} (α :=
      tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
      (CategoryStruct.comp (Y := biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
          (biproduct.lift fun (j : J) ↦ X ◁ biproduct.π f j)
          (biproduct.π (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j) :
        tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
      (CategoryStruct.comp (Y := biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
          (∑ j : J,
            X ◁ biproduct.π f j ≫
              biproduct.ι.{0, v_1, u_1} (C := C) (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j)
          (biproduct.π (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j) :
        tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
⊢ Eq.{v_1 + 1} (α :=
    tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶
      biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
    (Iso.hom (leftDistributor X f) :
      tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶
        biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
    (∑ j : J,
        X ◁ biproduct.π f j ≫
          biproduct.ι.{0, v_1, u_1} (C := C) (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j :
      tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶
        biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
have w₂ : ∀ (j : J),
  Eq.{v_1 + 1} (α :=
    tensorObj.{v_1, u_1} (𝒞 := inst) X (biproduct.{0, v_1, u_1} f) ⟶ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
    (X ◁ biproduct.π f j)
    (CategoryStruct.comp (Y := biproduct.{0, v_1, u_1} fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j))
      (∑ j : J,
        X ◁ biproduct.π f j ≫
          biproduct.ι.{0, v_1, u_1} (C := C) (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j)
      (biproduct.π (fun (j : J) ↦ tensorObj.{v_1, u_1} (𝒞 := inst) X (f j)) j))
Tactic: classical
  ext
  dsimp [leftDistributor, Functor.mapBiproduct, Functor.mapBicone]
  erw [biproduct.lift_π]
  simp only [Preadditive.sum_comp, Category.assoc, biproduct.ι_π, comp_dite, comp_zero,
    Finset.sum_dite_eq', Finset.mem_univ, ite_true, eqToHom_refl, Category.comp_id]