Complex two square sub one norm sq ge seven

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.complex_two_square_sub_one_norm_sq_ge_seven
    (r : ℂ) (hr : 1 ≤ ‖r‖) (hp : 1 ≤ ‖r + 1‖) (hm : 1 ≤ ‖r - 1‖) :
    7 ≤ ‖(2 : ℂ) * r ^ 2 - 1‖ ^ 2 := by sorry





end D1Bound5
end