Coupled phase geometry

import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Tactic
import Definitions.Def_D1Bound5_CoupledPhaseGeometry_Definitions

section
namespace D1Bound5








theorem _root_.D1Bound5.coupled_phase_geometry (a b s : ℂ) (q : ℝ)
    (hq : 1 ≤ q) (hB : 0 < ‖b‖) (hBS : ‖b‖ ≤ ‖s‖)
    (hsep : q*‖a‖ ≤ ‖b‖) :
    ∃ x : ℝ, 0 ≤ x ∧ x ≤ 2 ∧
      (phaseVandermondeRatio a b s)^2*phasePhi b s ≤ coupledPhasePolynomial q x := by sorry

end D1Bound5
end