An asymmetric weighted pairwise ratio sum is at least four

Proved

WorkbookSource.base_27490

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

lean-workbooksource-checked

Prove that for any three positive reals a, b, c, the following inequality holds: $\frac{2a}{b+c}+\frac{6b}{c+a}+\frac{3c}{a+b} \ge 4$

Source: InternLM Lean-Workbook, record lean_workbook_27490 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_27490 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (2 * a / (b + c) + 6 * b / (c + a) + 3 * c / (a + b)) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_27490; Apache-2.0

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