Small Pair Seeds 43 checked

Proved

D1Bound5.smallPairSeeds_43_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallPairSeeds_43_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_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs43_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs43_Definitions_002
import Definitions.Def_D1Bound5_TwoSmallSeedDisks_Definitions

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

theorem _root_.D1Bound5.smallPairSeeds_43_checked :
    pairSeedsCoveredBool smallPairA_43 smallPairB_43
      seedRootDisk_1_3 smallPairClosure_43 = true := by sorry





end D1Bound5
end

Source

D1Bound5/SmallPairGraphArithmetic43.lean, lines 8-11, SHA-256 e5f34b379ce5169c43ac116b737d74c40f2d6c8e9799f87b666db23e5ef5c3f2. Project: https://github.com/tomislav-math/d1-bound5-lean

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