Finite PLeading norm le

Proved

D1Bound5.finitePLeading_norm_le

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

diophantine-tuplesnumber-theory

Auxiliary result finitePLeading_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.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FinitePResidualIdentity_Definitions

Formal statement

section
open Finset

namespace D1Bound5

attribute [local simp] Matrix.cons_val_two Matrix.cons_val_three













theorem _root_.D1Bound5.finitePLeading_norm_le (a b s : ℂ)
    (hA : 1 ≤ ‖a‖) (hAB : ‖a‖ ≤ ‖b‖) (hBS : ‖b‖ ≤ ‖s‖) (i : Fin 4) :
    ‖finitePLeading a b s i‖ ≤ (35/16 : ℝ)*‖s‖^2/‖a‖^3 := by sorry

end D1Bound5
end

Source

D1Bound5/FinitePLeadingBound.lean, lines 49-88, SHA-256 237162555cf7aab44715f5fa900788556d3bb32195d23d9b5b35cca9462a87fc. Project: https://github.com/tomislav-math/d1-bound5-lean

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