lean_workbook_plus_74691

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

$27(3a^3+3b^3+3c^3+7abc) \ge 16(a+b+c)^3$ $\iff 65\sum a^3+93abc \ge 48\sum ab(a+b)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_74691 (a b c : ℝ) : 27 * (3 * a ^ 3 + 3 * b ^ 3 + 3 * c ^ 3 + 7 * a * b * c) ≥ 16 * (a + b + c) ^ 3 ↔ 65 * (a ^ 3 + b ^ 3 + c ^ 3) + 93 * a * b * c ≥ 48 * (a * b * (a + b) + b * c * (b + c) + c * a * (c + a))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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