A sixth-power bound for a product of symmetric sums

Proved

WorkbookSource.base_11000

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

lean-workbooksource-checked

If $a,b,c$ are positive reals,prove that: $(a+b+c)^6\geq 27(a^2+b^2+c^2)(ab+bc+ca)^2$

Source: InternLM Lean-Workbook, record lean_workbook_11000 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_11000 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a + b + c) ^ 6 ≥ 27 * (a ^ 2 + b ^ 2 + c ^ 2) * (a * b + b * c + c * a) ^ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_11000; Apache-2.0

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