Quad Int — norm nonneg

Proved

D1Bound5.QuadInt.norm_nonneg

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

diophantine-tuplesnumber-theory

Auxiliary result QuadInt.norm_nonneg in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

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.norm_nonneg (hd : 0 < discriminant tau nu) (z : QuadInt tau nu) :
    0 ≤ z.norm := by sorry









end QuadInt
end D1Bound5
end

Source

D1Bound5/Coordinates.lean, lines 30-34, SHA-256 da0cb0c42a6044e813dcdaaa1831735e6baddba8fa16b037f5289e53bcfae065. Project: https://github.com/tomislav-math/d1-bound5-lean

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