Pair Graph Prepared22 — indexed checked

Proved

D1Bound5.PairGraphPrepared22.indexed_checked

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

diophantine-tuplesnumber-theory

Auxiliary result PairGraphPrepared22.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.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_PairClosureIndexedWitness_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphInputs22_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphInputs22_Definitions_002
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData22_Definitions_001
import Definitions.Def_D1Bound5_SmallPairGraphWitnessData22_Definitions_003

Formal statement

section
set_option autoImplicit false

namespace D1Bound5
set_option maxRecDepth 100000
set_option maxHeartbeats 0

open PairGraphPrepared22

theorem _root_.D1Bound5.PairGraphPrepared22.indexed_checked :
    pairClosureIndexedWitnessBool smallPairA_22 smallPairB_22 anchorRoot
      (10^1100) smallPairClosure_22 witnesses destinations = true := by sorry



end D1Bound5
end

Source

D1Bound5/SmallPairGraphClosure22.lean, lines 19-103, SHA-256 1ad5c144188014238a603cfc8b0bd2d1c22589652257fbede20b4eafce2a9f80. Project: https://github.com/tomislav-math/d1-bound5-lean

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