A shifted cyclic reciprocal sum is at least one

Proved

WorkbookSource.plus_55771

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

lean-workbooksource-checked

For positive reals $a, b, c$ such that $a + b + c = 3$ . Prove that: $\\sum_{cyc}{\\frac {a}{b^2 + 2}}\\ge 1$

Source: InternLM Lean-Workbook, record lean_workbook_plus_55771 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_55771 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a / (b ^ 2 + 2) + b / (c ^ 2 + 2) + c / (a ^ 2 + 2) ≥ 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_55771; Apache-2.0

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