A normalized triple product bounded by pairwise products

Proved

WorkbookSource.base_26655

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

lean-workbooksource-checked

Let $a,b,c>0,a+b+c=3$ , prove that: $24\frac{abc}{(a+b)(b+c)(c+a)}\le cb+ac+ba$

Source: InternLM Lean-Workbook, record lean_workbook_26655 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_26655 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : 24 * (a * b * c) / (a + b) / (b + c) / (c + a) ≤ b * c + a * c + a * b  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_26655; Apache-2.0

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