(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    (α : Type w) →
      [inst_1 : CategoryTheory.Limits.HasFiniteProducts C] →
        [inst_2 : CategoryTheory.Limits.HasLimitsOfShape (Finset (CategoryTheory.Discrete α))ᵒᵖ C] →
          [inst_3 : CategoryTheory.Limits.HasLimitsOfShape (CategoryTheory.Discrete α) C] →
            (CategoryTheory.Limits.ProductsFromFiniteCofiltered.liftToFinset C α).comp CategoryTheory.Limits.lim ≅
              CategoryTheory.Limits.lim