Half Binomial Coeff abs antitone

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_HalfBinomialCoefficients_Definitions

section
open Finset

namespace D1Bound5










theorem _root_.D1Bound5.halfBinomialCoeff_abs_antitone
    {j k : ℕ} (hj : 1 ≤ j) (hjk : j ≤ k) :
    |halfBinomialCoeff k| ≤ |halfBinomialCoeff j| := by sorry







end D1Bound5
end