Finite A4 root columns norm le

Proved

D1Bound5.finiteA4_root_columns_norm_le

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finiteA4_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
import Mathlib.Tactic.Convert
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteA4Coefficients_Definitions
import Definitions.Def_D1Bound5_FiniteA4Matrix_Definitions

Formal statement

section
namespace D1Bound5







theorem _root_.D1Bound5.finiteA4_root_columns_norm_le (x y c : ℂ) (hxy : ‖x‖ ≤ ‖y‖) (i : Fin 3) :
    ‖finiteA4Left x y c i‖+‖finiteA4Right x y c i‖ ≤
      ‖y‖^5*∑ ell : Fin 5, (finiteA4CoefficientSums i ell : ℝ)*(‖y‖*‖c‖)^(ell : ℕ) := by sorry



end D1Bound5
end

Source

D1Bound5/FiniteA4Height.lean, lines 48-58, SHA-256 9a08f5646dc099fdc32895a9f25b5747a42057d2621384971697b0f7dffad0bf. Project: https://github.com/tomislav-math/d1-bound5-lean

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