Full small pair model allowed
ProvedD1Bound5.full_small_pair_model_alloweddiophantine-tuplesnumber-theory
Maximality excludes the five extraneous coordinate orders in the finite rectangle. It is used only here, after complete finite-order classification.
Preamble
import Mathlib.Algebra.Group.Int.Units import Mathlib.Algebra.Polynomial.Monic import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Algebra.Squarefree.Basic import Mathlib.Analysis.Complex.Norm import Mathlib.Data.Fin.Tuple.Sort import Mathlib.Data.Finset.Card import Mathlib.Data.Finset.Prod import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Int.GCD import Mathlib.Data.Int.Interval import Mathlib.Data.Int.Sqrt import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.IntervalCases import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Definitions.Def_D1Bound5_Coordinates_Definitions import Definitions.Def_D1Bound5_SmallPairClassification_Definitions
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
open QuadInt
theorem _root_.D1Bound5.full_small_pair_model_allowed
{K : Type*} [Field K] [NumberField K]
{tau nu : ℤ} (e : QuadInt tau nu ≃+* 𝓞 K)
(htau : tau = 0 ∨ tau = 1) (hd : 0 < discriminant tau nu)
(hlo : 1 ≤ nu) (hhi : nu ≤ 8) : (tau,nu) ∈ smallPairModels := by sorry
end D1Bound5
end
Source
D1Bound5/SmallPairClassification.lean, lines 16-50, SHA-256 a32a3e7b2d5dfed4754fd2fe6af26c9e86156fe171110d66d6c2f3d17661c981. Project: https://github.com/tomislav-math/d1-bound5-lean