Small Triple Closure 9 checked

Proved

D1Bound5.smallTripleClosure_9_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallTripleClosure_9_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.Data.List.Range
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallTripleExtensionData9_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 8000000











theorem _root_.D1Bound5.smallTripleClosure_9_checked :
    pairClosureBool smallTripleAnchorA_9 smallTripleAnchorB_9
      (10^80) smallTriplePairClosure_9 = true := by sorry





end D1Bound5
end

Source

D1Bound5/SmallTripleExtensionData9.lean, lines 107-110, SHA-256 d547b2c59760d0754a4660f0e6f6a2dd995b480c12bf4f53eac6fc574c6b3772. Project: https://github.com/tomislav-math/d1-bound5-lean

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