A six-term four-variable cyclic ratio sum is at least four

Proved

WorkbookSource.base_52622

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

lean-workbooksource-checked

a,b,c,d >0 ,prove that:

$\frac{a}{a+b}+\frac{c}{c+d}+\frac{a}{b+c}+\frac{2b}{c+d}+\frac{c}{d+a}+\frac{2d}{a+b}\geq 4.$

Source: InternLM Lean-Workbook, record lean_workbook_52622 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_52622 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a / (a + b) + c / (c + d) + a / (b + c) + 2 * b / (c + d) + c / (d + a) + 2 * d / (a + b)) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_52622; Apache-2.0

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