Norm sq eq absolute norm

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.QuadraticAlgebra.NormDeterminant
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.norm_sq_eq_absolute_norm {K : Type*} [Field K] [NumberField K]
    [NumberField.IsTotallyComplex K] (hK : finrank ℚ K = 2) (φ : K →+* ℂ) (x : 𝓞 K) :
    ‖φ (x : K)‖^2 = (Algebra.norm ℤ x : ℝ) := by sorry

end D1Bound5
end