Prove2Me

Small Pair Filter 46 checked

Proved
D1Bound5.smallPairFilter_46_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairFilter_46_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_SmallPairGraphInputs46_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs46_Definitions_002
Formal statement
section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.smallPairFilter_46_checked :
    largePairVertices smallPairA_46 smallPairB_46 smallPairClosure_46 = smallPairLarge_46 := by sorry



end D1Bound5
end
Source
D1Bound5/SmallPairGraphArithmetic46.lean, lines 13-15, SHA-256 f9a32640a9b051fd190da9bbb41a14d597818d62631e660bf974bcf2f782f93c. Project: https://github.com/tomislav-math/d1-bound5-lean

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