Prove2Me

Pair Graph Prepared19 — indexed checked

Proved
D1Bound5.PairGraphPrepared19.indexed_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared19.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_SmallPairGraphInputs19_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs19_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData19_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData19_Definitions_003
Formal statement
section
namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared19

theorem _root_.D1Bound5.PairGraphPrepared19.indexed_checked :
    pairClosureIndexedWitnessBool smallPairA_19 smallPairB_19 anchorRoot
      (10^1100) smallPairClosure_19 witnesses destinations = true := by sorry



end D1Bound5
end
Source
D1Bound5/SmallPairGraphClosure19.lean, lines 23-116, SHA-256 b30398822eeed7098ccbea3abf18123621d25d3edf023bff9cf8d592bd359619. Project: https://github.com/tomislav-math/d1-bound5-lean

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