A shifted pairwise reciprocal lower bound at fixed sum three

Proved

WorkbookSource.base_9620

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

lean-workbooksource-checked

Let $a,b,c>0$ such that $a+b+c=3$ . Prove that: $\sum_{cyc} \frac{a+b}{ab+3}\ge \frac{3}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_9620 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_9620 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : (a + b) / (a * b + 3) + (b + c) / (b * c + 3) + (c + a) / (c * a + 3) ≥ 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9620; Apache-2.0

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