Pair Light Indexed Witnesses Checked Bool eq

import Init
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_PairClosureIndexedWitness_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions
import Definitions.Def_D1Bound5_PairLightArithmeticBridge_Definitions
import Definitions.Def_D1Bound5_PairLightArithmetic_Definitions
import Definitions.Def_D1Bound5_PairLightClosureBridge_Definitions
import Definitions.Def_D1Bound5_PairLightClosure_Definitions

section
namespace D1Bound5














theorem _root_.D1Bound5.pairLightIndexedWitnessesCheckedBool_eq {tau nu : ℤ}
    (a b r0 : QuadInt tau nu) (bound : ℤ) (vertices : List (QuadInt tau nu))
    (witnesses : List (PairRootWitness tau nu))
    (destinations : List (Option Nat × Option Nat)) :
    pairLightIndexedWitnessesCheckedBool tau nu
      (pairLightCoordinates a) (pairLightCoordinates b) (pairLightCoordinates r0) bound
      (vertices.map pairLightCoordinates) (witnesses.map pairLightRootWitnessCoordinates)
      destinations =
      pairIndexedWitnessesCheckedBool a b r0 bound vertices witnesses destinations := by sorry

end D1Bound5
end