Half Binomial Weighted Coeff norm le

import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Definitions.Def_D1Bound5_ComplexHalfBinomial_Definitions
import Definitions.Def_D1Bound5_HalfBinomialCoefficients_Definitions

section
open Finset

namespace D1Bound5




theorem _root_.D1Bound5.halfBinomialWeightedCoeff_norm_le
    (x y : ℂ) (t : ℝ) (ht : 0 ≤ t)
    (hx : ‖x‖ ≤ t) (hy : ‖y‖ ≤ t)
    (n : ℕ) (hn : 2 ≤ n) :
    ‖halfBinomialWeightedCoeff x y n‖ ≤
      4 * |halfBinomialCoeff n| * t ^ n := by sorry





end D1Bound5
end