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Quad Int — discriminant le four bound

Proved
D1Bound5.QuadInt.discriminant_le_four_bound

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

diophantine-tuplesnumber-theory

A nonreal element in a bounded disk bounds the field discriminant. Used for the Delta<=60 reduction in lem:tail-irregular.

Preamble
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Tactic.Linarith
import Definitions.Def_D1Bound5_Coordinates_Definitions

Formal statement
section
namespace D1Bound5



namespace QuadInt

variable {tau nu : ℤ}
















theorem _root_.D1Bound5.QuadInt.discriminant_le_four_bound (hd : 0 < discriminant tau nu)
    {z : QuadInt tau nu} {M : ℤ} (hM : z.norm ≤ M) (hy : z.im ≠ 0) :
    discriminant tau nu ≤ 4*M := by sorry

end QuadInt
end D1Bound5
end
Source
D1Bound5/Coordinates.lean, lines 64-73, SHA-256 da0cb0c42a6044e813dcdaaa1831735e6baddba8fa16b037f5289e53bcfae065. Project: https://github.com/tomislav-math/d1-bound5-lean

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