Pair Indexed Witnesses Checked Bool eq prefix drop

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_PairClosureIndexedChunks_Definitions
import Definitions.Def_D1Bound5_PairClosureIndexedWitness_Definitions
import Definitions.Def_D1Bound5_PairClosureWitness_Definitions

section
namespace D1Bound5
open QuadInt




theorem _root_.D1Bound5.pairIndexedWitnessesCheckedBool_eq_prefix_drop {tau nu : ℤ}
    (a b r0 : QuadInt tau nu) (bound : ℤ) (vertices : List (QuadInt tau nu))
    (n : ℕ) (witnesses : List (PairRootWitness tau nu))
    (destinations : List (Option Nat × Option Nat)) :
    pairIndexedWitnessesCheckedBool a b r0 bound vertices witnesses destinations =
      (pairIndexedWitnessesPrefixBool a b r0 bound vertices n witnesses destinations &&
        pairIndexedWitnessesCheckedBool a b r0 bound vertices
          (witnesses.drop n) (destinations.drop n)) := by sorry







end D1Bound5
end