{J : Type w} →
  {C : Type u} →
    [inst : CategoryTheory.Category.{v, u} C] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
        (f : J → C) →
          (i : J) →
            [inst_2 : CategoryTheory.Limits.HasBiproduct f] →
              [inst_3 : CategoryTheory.Limits.HasBiproduct (Subtype.restrict (fun j => j ≠ i) f)] →
                CategoryTheory.Limits.kernel (CategoryTheory.Limits.biproduct.π f i) ≅
                  ⨁ Subtype.restrict (fun j => j ≠ i) f