Pair Closure of witness checked

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_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions

section
namespace D1Bound5
open QuadInt


















theorem _root_.D1Bound5.pairClosure_of_witness_checked {tau nu : ℤ}
    (hd : 0 < discriminant tau nu) (a b r0 : QuadInt tau nu)
    (bound : ℤ) (vertices : List (QuadInt tau nu))
    (witnesses : List (PairRootWitness tau nu))
    (hcheck : pairClosureWitnessBool a b r0 bound vertices witnesses = true)
    {z w : QuadInt tau nu} (hz : z ∈ vertices)
    (hw : w = pairMutationPlus a b z ∨ w = pairMutationMinus a b z)
    (hbound : w.norm ≤ bound) : w ∈ vertices := by sorry



end D1Bound5
end