Half Binomial Coeff signed pair nonneg

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_signed_pair_nonneg (i j : ℕ) :
    0 ≤ (-1 : ℝ) ^ (i + j + 2) *
      (halfBinomialCoeff (i + 1) * halfBinomialCoeff (j + 1)) := by sorry



end D1Bound5
end