Is D1 — card le four of one three negative
ProvedD1Bound5.IsD1.card_le_four_of_one_three_negativediophantine-tuplesnumber-theory
Complete negative-entry branch of the manuscript's {1,3} lemma, over all imaginary quadratic full rings. The extra entry may be -1.
Preamble
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.Finset.Card import Mathlib.Data.Fintype.EquivFin import Mathlib.Data.Int.GCD 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_IsD1
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.IsD1.card_le_four_of_one_three_negative
{K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
(hK : finrank ℚ K = 2) {A : Finset (𝓞 K)} (hA : IsD1 A)
(h1 : (1 : 𝓞 K) ∈ A) (h3 : (3 : 𝓞 K) ∈ A)
(hn : ∃ n : ℤ, n<0 ∧ (n : 𝓞 K) ∈ A) : A.card ≤ 4 := by sorry
end D1Bound5
end
Source
D1Bound5/OneThreeNegative.lean, lines 179-239, SHA-256 608590903d9651b83081c7c7b14962c497bd29944ae7411568eb23eee5734f08. Project: https://github.com/tomislav-math/d1-bound5-lean