Trace zero no three tau zero

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_Coordinates_Definitions

section
namespace D1Bound5












theorem _root_.D1Bound5.trace_zero_no_three_tau_zero {nu : ℤ} (hnu : 1 < nu)
    (x y z : QuadInt 0 nu) (hx0 : x ≠ 0) (hy0 : y ≠ 0) (hz0 : z ≠ 0)
    (hx : 2 * x.re = 0) (hy : 2 * y.re = 0) (hz : 2 * z.re = 0)
    (hxy : ∃ r : QuadInt 0 nu, r * r = x * y + 1)
    (hxz : ∃ r : QuadInt 0 nu, r * r = x * z + 1)
    (hyz : ∃ r : QuadInt 0 nu, r * r = y * z + 1) : False := by sorry











end D1Bound5
end