Prove2Me

The sign of a rational polynomial expression

Proved
WorkbookSource.problem_33282

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

we have (∀a≤43):(3a−4)(3a−1)250(1+a2)≤0(\forall a\le \frac{4}{3}):\frac{(3a-4)(3a-1)^2}{50(1+a^2)}\le0

Source: InternLM Lean-Workbook, record lean_workbook_33282 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_33282 : ∀ a ≤ (4:ℝ) / 3, (3 * a - 4) * (3 * a - 1) ^ 2 / (50 * (1 + a ^ 2)) ≤ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33282; Apache-2.0

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