An asymmetric cubic bound with coefficients nine and fourteen

Proved

WorkbookSource.base_2640

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

lean-workbooksource-checked

Show that $9a^2b+a^2c+9ab^2+ac^2+b^2c+bc^2 \ge 14abc$ given $a, b, c>0$

Source: InternLM Lean-Workbook, record lean_workbook_2640 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2640 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 9 * a ^ 2 * b + a ^ 2 * c + 9 * a * b ^ 2 + a * c ^ 2 + b ^ 2 * c + b * c ^ 2 ≥ 14 * a * b * c  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2640; Apache-2.0

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