Is D1 — one three small third eq eight

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.Fintype.EquivFin
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.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_IsD1

section
open scoped NumberField Classical
open Module

namespace D1Bound5




theorem _root_.D1Bound5.IsD1.one_three_small_third_eq_eight
    {K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) (phi : K →+* ℂ)
    {A : Finset (𝓞 K)} (hA : IsD1 A)
    (h1 : (1 : 𝓞 K) ∈ A) (h3 : (3 : 𝓞 K) ∈ A) (hcard : 4 < A.card)
    (z : 𝓞 K) (hz : z ∈ A) (hz1 : z ≠ 1) (hz3 : z ≠ 3)
    (hlo : 9 ≤ ‖phi (z : K)‖^2) (hhi : ‖phi (z : K)‖^2 < 225) : z = 8 := by sorry



end D1Bound5
end