An alternating pair-sum ratio sum is at least four

Proved

WorkbookSource.base_2556

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

lean-workbooksource-checked

Prove for all positive reals a,b,c,d:

$\frac {a + c}{b + c} + \frac {b + d}{c + d} + \frac {c + a}{d + a} + \frac {d + b}{a + b}\ge 4$

Source: InternLM Lean-Workbook, record lean_workbook_2556 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2556 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a + c) / (b + c) + (b + d) / (c + d) + (c + a) / (d + a) + (d + b) / (a + b) ≥ 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_2556; Apache-2.0

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