Unit pair symmetric complex obstruction

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Finset.Card
import Mathlib.Data.Int.GCD
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination

section
open scoped NumberField
open Module

namespace D1Bound5




theorem _root_.D1Bound5.unit_pair_symmetric_complex_obstruction
    (a b G J : ℂ) (hA : 3 ≤ ‖a‖) (hAB : ‖a‖ ≤ ‖b‖)
    (hG : G = 2 * a ^ 2 * b ^ 2 - a ^ 2 - 1)
    (hid : (G - J) * (G + J) = (a ^ 2 - 1) ^ 2)
    (hm : 1 ≤ ‖G - J‖) (hp : 1 ≤ ‖G + J‖) : False := by sorry







end D1Bound5
end