Finite A3 root columns norm le

Proved

D1Bound5.finiteA3_root_columns_norm_le

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

diophantine-tuplesnumber-theory

Auxiliary result finiteA3_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_FiniteA3Coefficients_Definitions
import Definitions.Def_D1Bound5_FiniteA3Matrix_Definitions

Formal statement

section
namespace D1Bound5







theorem _root_.D1Bound5.finiteA3_root_columns_norm_le (x y c : ℂ) (hxy : ‖x‖ ≤ ‖y‖) (i : Fin 3) :
    ‖finiteA3Left x y c i‖+‖finiteA3Right x y c i‖ ≤
      ‖y‖^3*∑ ell : Fin 4, (finiteA3CoefficientSums i ell : ℝ)*(‖y‖*‖c‖)^(ell : ℕ) := by sorry



end D1Bound5
end

Source

D1Bound5/FiniteA3Height.lean, lines 43-53, SHA-256 f804d9c0c6b4a710739b80930e84355ca29a061e137634a0fae8411054c3b698. Project: https://github.com/tomislav-math/d1-bound5-lean

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