Prove2Me

A sharp cubic bound for a cyclic mixed sum

Proved
WorkbookSource.base_876

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let a,b,c≥0.a, b,c\geq 0 . Prove that (a+b+c)3≥274(a2b+b2c+c2a)(a+b+c)^3\geq\frac{27}{4}(a^2b+b^2c+c^2a)

Source: InternLM Lean-Workbook, record lean_workbook_876 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_876 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) : (a + b + c) ^ 3 ≥ (27 / 4) * (a ^ 2 * b + b ^ 2 * c + c ^ 2 * a)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_876; Apache-2.0

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