Mutate eq canonical

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_DescentAlgebra_Definitions
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions

section
namespace D1Bound5
open QuadInt
























theorem _root_.D1Bound5.mutate_eq_canonical {tau nu : ℤ} (hd : 0 < discriminant tau nu)
    (a b z r0 r s : QuadInt tau nu)
    (h0 : r0*r0 = a*b+1) (hr : r*r = a*z+1) (hs : s*s = b*z+1) :
    mutate a b z r0 r s = pairMutationPlus a b z ∨
    mutate a b z r0 r s = pairMutationMinus a b z := by sorry











end D1Bound5
end