Finite A4Ratio Weights nonneg

Proved

D1Bound5.finiteA4RatioWeights_nonneg

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

diophantine-tuplesnumber-theory

Auxiliary result finiteA4RatioWeights_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.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_FiniteA4RatioHeight_Definitions

Formal statement

section
noncomputable section

namespace D1Bound5





theorem _root_.D1Bound5.finiteA4RatioWeights_nonneg (r : ℝ) (hr : 0 ≤ r) (i : Fin 3) (ell : Fin 5) :
    0 ≤ finiteA4RatioWeights r i ell := by sorry







end D1Bound5
end

Source

D1Bound5/FiniteA4RatioHeight.lean, lines 17-29, SHA-256 a98d9593d896e1b8a0048726d24791b93b2bacc8fb14d4196e608cc3b8ddd02c. Project: https://github.com/tomislav-math/d1-bound5-lean

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