Bennett Cleared Residue remove node

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettClearedResidues_Definitions

section
open Finset

namespace D1Bound5

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









section Nodes

variable {I : Type*} [DecidableEq I]










theorem _root_.D1Bound5.bennettClearedResidue_remove_node (s : Finset I) (a : I → F)
    (k : ℕ) (ν : F) (i j q : I) (hq : q ∈ s)
    (hiq : i ≠ q) (hjq : j ≠ q) (ha : a j ≠ a q) :
    (bennettClearedResidue s a k ν i j).eval (-a q) =
      ((a j - a q)⁻¹) ^ k *
        (bennettClearedResidue (s.erase q) a k (ν - (k : F)) i j).eval (-a q) := by sorry







end Nodes

end D1Bound5
end