Bennett Two Cleared Entry eq scaled residue

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.Combinatorics.Enumerative.Catalan.Basic
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettResiduePolynomials_Definitions
import Definitions.Def_D1Bound5_BennettTwoIntegralEntries_Definitions

section
open Finset

namespace D1Bound5

variable {F : Type*} [Field F] [CharZero F]


























theorem _root_.D1Bound5.bennettTwoClearedEntry_eq_scaled_residue
    (a b c : F) (ha : a ≠ 0) (hb : b ≠ 0) (hc : c ≠ 0)
    (k : ℕ) (i j : Fin 3) :
    bennettTwoClearedEntry a b c k i j =
      (4 * (a * b) ^ 2 * c * (a - b) ^ 2) ^ k *
        (bennettPolynomialResidue Finset.univ (bennettTwoNodes a b) k (1 / 2 : F)
          i j).eval ((a * b * c)⁻¹) := by sorry



end D1Bound5
end