Full ring three negative odd impossible

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

section
open scoped NumberField
open Module

namespace D1Bound5

























theorem _root_.D1Bound5.full_ring_three_negative_odd_impossible
    {K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) (x y z : ℤ)
    (hx : x<0) (hy : y<0) (hz : z<0)
    (hxo : x%2=1) (hyo : y%2=1) (hzo : z%2=1)
    (hxy : ∃ r : 𝓞 K, r*r = (x : 𝓞 K)*(y : 𝓞 K)+1)
    (hxz : ∃ r : 𝓞 K, r*r = (x : 𝓞 K)*(z : 𝓞 K)+1)
    (hyz : ∃ r : 𝓞 K, r*r = (y : 𝓞 K)*(z : 𝓞 K)+1) : False := by sorry






end D1Bound5
end