Pair Selected Cached Mask Nat Reject Bool eq

Proved

D1Bound5.pairSelectedCachedMaskNatRejectBool_eq

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

diophantine-tuplesnumber-theory

Auxiliary result pairSelectedCachedMaskNatRejectBool_eq in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

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_PairRawSelectedFloorWitnesses_Definitions
import Definitions.Def_D1Bound5_PairSelectedCachedMask_Definitions

Formal statement

section
namespace D1Bound5



theorem _root_.D1Bound5.pairSelectedCachedMaskNatRejectBool_eq (tau nu : ℤ)
    (sieve : List (ℕ × ℕ)) (xs ys : List (ℕ × ℕ)) (i : ℕ) :
    pairSelectedCachedMaskNatRejectBool tau nu sieve xs ys i =
      pairSelectedCachedMaskRejectBool tau nu sieve xs ys i := by sorry















end D1Bound5
end

Source

D1Bound5/PairRawSelectedFloorWitnesses.lean, lines 14-25, SHA-256 16663ee7ed18799dce07207a0b374d05787f04c1c37fca43ad73b4907ad0a013. Project: https://github.com/tomislav-math/d1-bound5-lean

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