Coherent half binomial manuscript tail norm le

import Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Lagrange
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 Polynomial

namespace D1Bound5













end D1Bound5




open Finset

namespace D1Bound5



end D1Bound5




open Finset

namespace D1Bound5


theorem _root_.D1Bound5.coherent_half_binomial_manuscript_tail_norm_le
    {ι : Type*} [DecidableEq ι]
    (s : Finset ι) (a : ι → ℂ) (hs : s.Nonempty)
    (x y : ℂ) (A P : ℝ)
    (hA : 0 < A) (hP : 0 < P)
    (ha : ∀ i ∈ s, A ≤ ‖a i‖)
    (hx : ‖x‖ ≤ 1 / P) (hy : ‖y‖ ≤ 1 / P)
    (hAP : 1 < A * P) :
    Summable (fun j : ℕ => halfBinomialWeightedCoeff x y (s.card + j) *
      MvPolynomial.aeval (fun i : s => (a i)⁻¹)
        (MvPolynomial.hsymm s ℂ j)) ∧
    ‖(∑' j : ℕ, halfBinomialWeightedCoeff x y (s.card + j) *
      MvPolynomial.aeval (fun i : s => (a i)⁻¹)
        (MvPolynomial.hsymm s ℂ j)) -
      halfBinomialWeightedCoeff x y s.card‖ ≤
      (4 * |halfBinomialCoeff (s.card + 1)|) / P ^ s.card *
        (1 / (1 - 1 / (A * P)) ^ s.card - 1) := by sorry



end D1Bound5




namespace D1Bound5









end D1Bound5
end