Growth quadratic negative
ProvedD1Bound5.growth_quadratic_negativediophantine-tuplesnumber-theory
Exact real endpoint estimates behind Lemma irregular-growth.
Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic import Mathlib.Algebra.Ring.Basic import Mathlib.Algebra.Ring.Equiv import Mathlib.Analysis.Complex.Norm import Mathlib.Data.Finset.Card import Mathlib.Data.Int.GCD import Mathlib.LinearAlgebra.Dimension.Free import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex import Mathlib.NumberTheory.NumberField.Norm import Mathlib.Tactic.Linarith import Mathlib.Tactic.LinearCombination import Mathlib.Tactic.Ring
Formal statement
section
open scoped NumberField
open Module
namespace D1Bound5
theorem _root_.D1Bound5.growth_quadratic_negative (A B C : ℝ) (hA : 3 ≤ A) (hAB : A ≤ B)
(hBC : B ≤ C) (hC : C ≤ 2*A*B) :
(A+B+C+1)^2+4-4*A*B*C < 0 := by sorry
end D1Bound5
end
Source
D1Bound5/IrregularGrowth.lean, lines 83-108, SHA-256 f449e549f059d0b5ff8d04afd421d9f1c8ec2bba64f1395f4efdedd79016bf4d. Project: https://github.com/tomislav-math/d1-bound5-lean