Small Triple classified rectangular

Proved

D1Bound5.smallTriple_classified_rectangular

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result smallTriple_classified_rectangular 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.IntervalCases
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_IsD1Tuple
import Definitions.Def_D1Bound5_SmallTripleCheck_Definitions
import Definitions.Def_D1Bound5_SmallTripleData_Definitions

Formal statement

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 6000000


























































































theorem _root_.D1Bound5.smallTriple_classified_rectangular {tau nu : ℤ}
    (htau : tau = 0 ∨ tau = 1) (hlo : 1 ≤ nu) (hhi : nu ≤ 8)
    (t : Fin 3 → QuadInt tau nu) (ht : IsD1Tuple t)
    (hnorm : ∀ i, (t i).norm ≤ 8) :
    tripleCoordinates (t 0) (t 1) (t 2) ∈ smallTripleTable tau nu := by sorry

end D1Bound5
end

Source

D1Bound5/SmallTripleData.lean, lines 329-352, SHA-256 d79644481c842f2a40b2f5554666f54fa185f12915c38d31e4f1b24ec16844da. Project: https://github.com/tomislav-math/d1-bound5-lean

View graph