Bennett Two Cleared Entry zero integral

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_BennettTwoIntegralEntries_Definitions

section
open Finset

namespace D1Bound5

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




















theorem _root_.D1Bound5.bennettTwoClearedEntry_zero_integral (S : Subring F)
    (a b c : F) (ha : a ∈ S) (hb : b ∈ S) (hc : c ∈ S)
    (ha0 : a ≠ 0) (hb0 : b ≠ 0) (k : ℕ) (hk : 1 ≤ k) (i : Fin 3) :
    ∃ q ∈ S, bennettTwoClearedEntry a b c k i 0 = 1 * q := by sorry









end D1Bound5
end