Prove2Me

Positivity of a sixth degree polynomial

Proved
WorkbookSource.problem_22210

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

lean-workbooksource-checked

If 0≤a≤10\leq a\leq 1 prove that 64a6−192a5+176a4−32a3+116a2−132a+223>0 64 a^6 - 192 a^5 + 176 a^4 - 32 a^3 + 116 a^2 - 132 a + 223>0 .

Source: InternLM Lean-Workbook, record lean_workbook_22210 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble
import Mathlib
open Real
Formal statement
theorem WorkbookSource.problem_22210 (a : ℝ) (ha : 0 ≤ a ∧ a ≤ 1) : 64 * a ^ 6 - 192 * a ^ 5 + 176 * a ^ 4 - 32 * a ^ 3 + 116 * a ^ 2 - 132 * a + 223 > 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_22210; Apache-2.0

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