Pair Closure Bool of indexed 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_PairClosureIndexedWitness_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions

section
namespace D1Bound5
open QuadInt


















theorem _root_.D1Bound5.pairClosureBool_of_indexed_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))
    (destinations : List (Option Nat × Option Nat))
    (hcheck : pairClosureIndexedWitnessBool a b r0 bound vertices witnesses destinations = true) :
    pairClosureBool a b bound vertices = true := by sorry

end D1Bound5
end