Pair Phase Pilot41 — filter checked

Proved

D1Bound5.PairPhasePilot41.filter_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairPhasePilot41.filter_checked 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.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_SmallPairGraphCheck_Definitions
import Definitions.Def_D1Bound5_SmallPairPhaseData41_Definitions

Formal statement

section
namespace D1Bound5.PairPhasePilot41
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.PairPhasePilot41.filter_checked :
    largePairVertices anchorA anchorB closure = large := by sorry

end D1Bound5.PairPhasePilot41
end

Source

D1Bound5/SmallPairPhaseFilter41.lean, lines 7-9, SHA-256 9ecc92bc986f020c3d76f9be28212db2423ee3fc22564c0b952bf487b6abb127. Project: https://github.com/tomislav-math/d1-bound5-lean

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