A shifted mixed product ratio upper bound

Proved

WorkbookSource.plus_6090

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

lean-workbooksource-checked

If $a,b,c > 0$ , then

$\frac {ab + 3c}{a + b + 2c} + \frac {ca + 3b}{a + 2b + c} + \frac {bc + 3a}{2a + b + c}\leq\frac {a + b + c + 9}{4}$

Source: InternLM Lean-Workbook, record lean_workbook_plus_6090 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_6090 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a * b + 3 * c) / (a + b + 2 * c) + (c * a + 3 * b) / (a + 2 * b + c) + (b * c + 3 * a) / (2 * a + b + c) ≤ (a + b + c + 9) / 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_6090; Apache-2.0

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