Finite N3 root columns norm le

Proved

D1Bound5.finiteN3_root_columns_norm_le

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

diophantine-tuplesnumber-theory

Auxiliary result finiteN3_root_columns_norm_le 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 Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteN3Matrix_Definitions

Formal statement

section
namespace D1Bound5
















theorem _root_.D1Bound5.finiteN3_root_columns_norm_le (x y c : ℂ) (hxy : ‖x‖ ≤ ‖y‖) (i : Fin 3) :
    ‖finiteN3Left x y c i‖+‖finiteN3Right x y c i‖ ≤
      342*‖y‖^4+2352*‖y‖^5*‖c‖+5792*‖y‖^6*‖c‖^2+4096*‖y‖^7*‖c‖^3 := by sorry





end D1Bound5
end

Source

D1Bound5/FiniteN3Height.lean, lines 66-95, SHA-256 f481f700219409141bd10895fbdbd58481a503388f7da4c50027895a33e66039. Project: https://github.com/tomislav-math/d1-bound5-lean

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