Pair Independent Bool of cached certificate

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_PairBipartiteCheck_Definitions
import Definitions.Def_D1Bound5_PairCachedResidues_Definitions

section
namespace D1Bound5


























theorem _root_.D1Bound5.pairIndependentBool_of_cached_certificate {tau nu : ℤ}
    (sieve : List (ℕ × ℕ)) (vertices : List (QuadInt tau nu))
    (cached : List (PairResidueVertex tau nu))
    (hcheck : pairCachedIndependentCertificateBool sieve vertices cached = true) :
    pairIndependentBool sieve vertices = true := by sorry

end D1Bound5
end