A cubic and quadratic symmetric bound at fixed sum one

Proved

WorkbookSource.base_34132

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

lean-workbooksource-checked

Prove this inequality $27abc+36(ab+bc+ca)\leq 13$ with $a,b,c \ge 0$ and $a+b+c=1$

Source: InternLM Lean-Workbook, record lean_workbook_34132 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_34132 (a b c : ℝ) (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (habc : a + b + c = 1) : 27 * a * b * c + 36 * (a * b + b * c + c * a) ≤ 13  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_34132; Apache-2.0

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