Prove2Me

Pair Phase Pilot41 — closure indexed witness checked

Proved
D1Bound5.PairPhasePilot41.closure_indexed_witness_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairPhasePilot41.closure_indexed_witness_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_SmallPairIndexedClosure41_Definitions
import Definitions.Def_D1Bound5_SmallPairPhaseData41_Definitions
import Definitions.Def_D1Bound5_SmallPairWitnessData41_Definitions
Formal statement
section
namespace D1Bound5.PairPhasePilot41
set_option maxRecDepth 100000
set_option maxHeartbeats 0



theorem _root_.D1Bound5.PairPhasePilot41.closure_indexed_witness_checked :
    pairClosureIndexedWitnessBool anchorA anchorB anchorRootWitness (10^1100)
      closure closureWitnesses indexedClosureDestinations = true := by sorry



end D1Bound5.PairPhasePilot41
end
Source
D1Bound5/SmallPairIndexedClosure41.lean, lines 385-388, SHA-256 aa955931a4521c8735423353db9d089a97667a50300a9fb2f5aca1b3277b29ee. Project: https://github.com/tomislav-math/d1-bound5-lean

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