A shifted weighted cyclic ratio sum is at least six

Proved

WorkbookSource.base_47380

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

lean-workbooksource-checked

For $a, b, c>0,$ prove that $\frac{5a+4b+c+2}{4b+c+1}+\frac{5b+4c+a+2}{4c+a+1}+\frac{5c+4a+b+2}{4a+b+1}\geq6$

Source: InternLM Lean-Workbook, record lean_workbook_47380 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_47380 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (5 * a + 4 * b + c + 2) / (4 * b + c + 1) + (5 * b + 4 * c + a + 2) / (4 * c + a + 1) + (5 * c + 4 * a + b + 2) / (4 * a + b + 1) ≥ 6  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_47380; Apache-2.0

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