Prove2Me

Pair Graph Prepared3 — indexed checked

Proved
D1Bound5.PairGraphPrepared3.indexed_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared3.indexed_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_PairClosureIndexedWitness_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs3_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs3_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData3_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData3_Definitions_003
Formal statement
section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared3

theorem _root_.D1Bound5.PairGraphPrepared3.indexed_checked :
    pairClosureIndexedWitnessBool smallPairA_3 smallPairB_3 anchorRoot
      (10^1100) smallPairClosure_3 witnesses destinations = true := by sorry



end D1Bound5
end
Source
D1Bound5/SmallPairGraphClosure3.lean, lines 22-109, SHA-256 6d15b89a2a116c6555da85d4cf9731182d4a4f7703df9c0da4d69aaff9714776. Project: https://github.com/tomislav-math/d1-bound5-lean

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