Finite Homogeneous Ratio Weight nonneg

Proved

D1Bound5.finiteHomogeneousRatioWeight_nonneg

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

diophantine-tuplesnumber-theory

Auxiliary result finiteHomogeneousRatioWeight_nonneg 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.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_FiniteHomogeneousRatio_Definitions

Formal statement

section
noncomputable section

namespace D1Bound5



theorem _root_.D1Bound5.finiteHomogeneousRatioWeight_nonneg (n : ℕ) (v : Fin (n+1) → ℤ)
    (r : ℝ) (hr : 0 ≤ r) : 0 ≤ finiteHomogeneousRatioWeight n v r := by sorry









end D1Bound5
end

Source

D1Bound5/FiniteHomogeneousRatio.lean, lines 10-12, SHA-256 15c96a58b594b4317eb87dac7d3be380eb2b464b0233e171dc57af6894fda59b. Project: https://github.com/tomislav-math/d1-bound5-lean

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