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Small Extension Symmetry norm

Proved
D1Bound5.smallExtensionSymmetry_norm

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

diophantine-tuplesnumber-theory

Auxiliary result smallExtensionSymmetry_norm 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.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.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Analysis.Complex.Polynomial.Basic
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.Data.List.Range
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_SmallExtensionSymmetry_Definitions

Formal statement
section
open scoped NumberField
open Module

namespace D1Bound5
open QuadInt















theorem _root_.D1Bound5.smallExtensionSymmetry_norm {tau nu : ℤ} (sgn conj : Bool)
    (z : QuadInt tau nu) : (smallExtensionSymmetry sgn conj z).norm = z.norm := by sorry











end D1Bound5
end
Source
D1Bound5/SmallExtensionSymmetry.lean, lines 75-78, SHA-256 67e063ccef711bfed6c0611c0e702166cb5f5a03a9533a5385fe57ef43b16f48. Project: https://github.com/tomislav-math/d1-bound5-lean

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