Bennett Homogeneous Series finset mul

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Group.Finset.Sigma
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.PartialFractions
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Algebra.Polynomial.RingDivision
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Sym.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettRepeatedHsymm_Definitions

section
open Finset

namespace D1Bound5

section Homogeneous

variable {R ι : Type*} [CommRing R] [DecidableEq ι]






theorem _root_.D1Bound5.bennettHomogeneousSeries_finset_mul
    (s : Finset ι) (a : ι → R) :
    (∏ i ∈ s, (1 - PowerSeries.C (a i) * PowerSeries.X)) *
      bennettHomogeneousSeries (fun i : s => a i) = 1 := by sorry



end Homogeneous

section Repeated

variable {F ι : Type*} [Field F] [CharZero F]
variable [Fintype ι] [DecidableEq ι]













end Repeated

end D1Bound5
end