Finite A4 root coefficient norm le

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteA4Coefficients_Definitions

section
namespace D1Bound5


theorem _root_.D1Bound5.finiteA4_root_coefficient_norm_le (x y : ℂ) (hxy : ‖x‖ ≤ ‖y‖)
    (i : Fin 3) (ell : Fin 5) :
    ‖finiteA4RootCoeff x y i 0 ell‖+‖finiteA4RootCoeff x y i 1 ell‖ ≤
      (finiteA4CoefficientSums i ell : ℝ)*‖y‖^(5+(ell : ℕ)) := by sorry









end D1Bound5
end