Nondegenerate small pair parameter bound

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Fin.Tuple.Sort
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Interval
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_Coordinates_Definitions

section
namespace D1Bound5
open QuadInt










theorem _root_.D1Bound5.nondegenerate_small_pair_parameter_bound {tau nu : ℤ}
    (htau : tau = 0 ∨ tau = 1) (hd : 0 < discriminant tau nu)
    (a b : QuadInt tau nu) (ha : a ≠ 0) (hb : b ≠ 0) (hab : a ≠ b)
    (hNa : a.norm ≤ 8) (hNb : b.norm ≤ 8)
    (hsquare : ∃ r, r*r = a*b+1) (hnondeg : a*b+1 ≠ 0) :
    discriminant tau nu ≤ 32 ∧ 1 ≤ nu ∧ nu ≤ 8 := by sorry

end D1Bound5
end