Small Pair Filter 3 checked

Proved

D1Bound5.smallPairFilter_3_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairFilter_3_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_SmallPairGraphInputs3_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs3_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphInputs3_Definitions_003

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.smallPairFilter_3_checked :
    largePairVertices smallPairA_3 smallPairB_3 smallPairClosure_3 = smallPairLarge_3 := by sorry



end D1Bound5
end

Source

D1Bound5/SmallPairGraphArithmetic3.lean, lines 13-15, SHA-256 a5595d899d140695b2f8be811778d9ea2f78cc8ff96425eb8c43a4bc305fc489. Project: https://github.com/tomislav-math/d1-bound5-lean

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