Small Pair Filter 23 checked

Proved

D1Bound5.smallPairFilter_23_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairFilter_23_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.List.Range
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_SmallPairGraphInputs23_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs23_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphInputs23_Definitions_003

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.smallPairFilter_23_checked :
    largePairVertices smallPairA_23 smallPairB_23 smallPairClosure_23 = smallPairLarge_23 := by sorry



end D1Bound5
end

Source

D1Bound5/SmallPairGraphArithmetic23.lean, lines 13-15, SHA-256 d47f8b0d8d49e0e0787d22d1aed13b248a747a1f313b9f5d1702b98a913fd3fb. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph