A four-variable cyclic pair-sum ratio is at least two

Proved

WorkbookSource.base_1693

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

lean-workbooksource-checked

Prove that for positive real numbers $a, b, c, d$ , the following inequality holds: $\frac{c}{a+b}+\frac{d}{b+c}+\frac{a}{c+d}+\frac{b}{d+a} \ge 2$

Source: InternLM Lean-Workbook, record lean_workbook_1693 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_1693 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (c / (a + b) + d / (b + c) + a / (c + d) + b / (d + a)) ≥ 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_1693; Apache-2.0

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