Full ring positive integer square

import Mathlib.Algebra.Polynomial.Monic
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Algebra.Squarefree.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Finset.Card
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Sqrt
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.full_ring_positive_integer_square {K : Type*} [Field K]
    [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) {m : ℤ} (hm : 0 < m)
    (hs : ∃ r : 𝓞 K, r*r = (m : 𝓞 K)) :
    ∃ n : ℤ, m = n^2 := by sorry



end D1Bound5
end