Small Triple Classified of explicit list
ProvedD1Bound5.smallTripleClassified_of_explicit_listdiophantine-tuplesnumber-theory
Soundness of the complete small-triple classifier.
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 Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_DiskEnumeration_Definitions import Definitions.Def_D1Bound5_IsD1Tuple import Definitions.Def_D1Bound5_SmallTripleCheck_Definitions
Formal statement
section
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.smallTripleClassified_of_explicit_list {tau nu : ℤ}
(hpos : 0 < discriminant tau nu)
(xs : List (QuadInt tau nu)) (rows : List (Finset (ℤ × ℤ)))
(cover : ∀ z ∈ disk tau nu 8, z ∈ xs)
(checked : smallTripleClassifiedBool xs rows = true)
(t : Fin 3 → QuadInt tau nu) (ht : IsD1Tuple t)
(hnorm : ∀ i, (t i).norm ≤ 8) :
tripleCoordinates (t 0) (t 1) (t 2) ∈ rows := by sorry
end D1Bound5
end
Source
D1Bound5/SmallTripleCheck.lean, lines 29-58, SHA-256 1f75bcdaa9e326145897ef273ea3989447fff478e71849b1db21c3aa9abd5c19. Project: https://github.com/tomislav-math/d1-bound5-lean