Small Triple Filter 6 checked

Proved

D1Bound5.smallTripleFilter_6_checked

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

diophantine-tuplesnumber-theory

Auxiliary result smallTripleFilter_6_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_SmallTripleExtensionData6_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 8000000













theorem _root_.D1Bound5.smallTripleFilter_6_checked :
    tripleExtensionFilterBool smallTripleAnchorA_6 smallTripleAnchorB_6
      smallTripleAnchorC_6 smallTriplePairClosure_6 smallTripleAllowed_6 = true := by sorry



end D1Bound5
end

Source

D1Bound5/SmallTripleExtensionData6.lean, lines 141-144, SHA-256 36f224d3730e31a0a51a42e087cb11043ed4d384f831a7959f50bfd1ed91e3aa. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph