Bennett two clear column zero

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

section
namespace D1Bound5

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




theorem _root_.D1Bound5.bennett_two_clear_column_zero
    (a b c : F) (ha : a ≠ 0) (hb : b ≠ 0)
    (k d0 d1 d2 h0 h1 h2 : ℕ) (hk : 1 ≤ k)
    (hd : d0 + d1 + d2 = 1) (hh : h0 + h1 + h2 + 1 = k + d0) :
    (a * b * (a - b) ^ 2) ^ k * (a * b * c) ^ (k - h0) *
        (b⁻¹) ^ (k + d1 + h1) * (a⁻¹) ^ (k + d2 + h2) =
      a ^ (d1 + h1) * b ^ (d2 + h2) * c ^ (k - h0) *
        (a - b) ^ (2 * k) := by sorry









end D1Bound5
end