Prove2Me

A cyclic squared pair-sum reciprocal lower bound

Proved
WorkbookSource.base_9398

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

lean-workbooksource-checked

Prove that 1(a+b)2+1(b+c)2+1(c+d)2+1(d+a)2≥2ac+bd\frac{1}{(a+b)^2}+\frac{1}{(b+c)^2}+\frac{1}{(c+d)^2}+\frac{1}{(d+a)^2}\ge \frac{2}{ac+bd} where a,b,c,d>0a,b,c,d>0.

Source: InternLM Lean-Workbook, record lean_workbook_9398 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_9398 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : 1 / (a + b) ^ 2 + 1 / (b + c) ^ 2 + 1 / (c + d) ^ 2 + 1 / (d + a) ^ 2 ≥ 2 / (a * c + b * d)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9398; Apache-2.0

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