A cyclic reciprocal-quadratic lower bound at fixed sum

Proved

WorkbookSource.base_117

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

lean-workbooksource-checked

Given $a,b,c>0$ and $a+b+c=3$ , prove that

\frac{b}{a^2+1}+\frac{c}{b^2+1}+\frac{a}{c^2+1}\geq\frac{3}{2}

Source: InternLM Lean-Workbook, record lean_workbook_117 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_117 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : (b / (a ^ 2 + 1) + c / (b ^ 2 + 1) + a / (c ^ 2 + 1)) ≥ 3 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_117; Apache-2.0

View graph