Pair Selected Cached Mask Reject Bool sound

Proved

D1Bound5.pairSelectedCachedMaskRejectBool_sound

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

One genuinely rejecting aligned conjunct makes the entire original cached sieve false. This is a statement about the exact old Boolean, so no signature-validity, mask-validity, or discriminant assumption is needed.

Preamble

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_PairCachedResidues_Definitions
import Definitions.Def_D1Bound5_PairSelectedCachedMask_Definitions

Formal statement

section
namespace D1Bound5




theorem _root_.D1Bound5.pairSelectedCachedMaskRejectBool_sound (tau nu : ℤ)
    (sieve : List (ℕ × ℕ)) (xs ys : List (ℕ × ℕ)) (i : ℕ)
    (hcheck : pairSelectedCachedMaskRejectBool tau nu sieve xs ys i = true) :
    pairCachedCoordinateSieveBool tau nu sieve xs ys = false := by sorry

end D1Bound5
end

Source

D1Bound5/PairSelectedCachedMask.lean, lines 14-55, SHA-256 842d5e0cce863d3301c8c65c34a04d2d07c08d156761bf506cdbbebcdd0db1f4. Project: https://github.com/tomislav-math/d1-bound5-lean

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