∀ (σ : Type u_1) (R : Type u_2) [inst : CommRing R] [inst_1 : DecidableEq σ] [inst_2 : Fintype σ] (k : ℕ)
  (f : Finset σ × σ → MvPolynomial σ R),
  ∑ t ∈ MvPolynomial.NewtonIdentities.pairs✝ σ k with t.1.card = k, f t =
    ∑ A ∈ Finset.powersetCard k Finset.univ, ∑ j ∈ A, f (A, j)