Discrete 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.discrete_two_square_sub_one_norm_sq_ge_seven
    {R : Type*} [CommRing R] (f : R →+* ℂ)
    (hdiscrete : ∀ x : R, x ≠ 0 → 1 ≤ ‖f x‖)
    (r : R) (hr : r ≠ 0) (hrsq : r ^ 2 ≠ 1) :
    7 ≤ ‖(2 : ℂ) * (f r) ^ 2 - 1‖ ^ 2 := by sorry



end D1Bound5
end