Pair Graph Prepared25 — indexed checked

Proved

D1Bound5.PairGraphPrepared25.indexed_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared25.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_SmallPairGraphInputs25_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs25_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData25_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData25_Definitions_003

Formal statement

section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared25

theorem _root_.D1Bound5.PairGraphPrepared25.indexed_checked :
    pairClosureIndexedWitnessBool smallPairA_25 smallPairB_25 anchorRoot
      (10^1100) smallPairClosure_25 witnesses destinations = true := by sorry



end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure25.lean, lines 21-102, SHA-256 d76b5a372dcc2a0a86abd57001a94b86fd9580c549192fe65cf554ec752528d1. Project: https://github.com/tomislav-math/d1-bound5-lean

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