A cyclic squared-reciprocal comparison at fixed sum three

Proved

WorkbookSource.base_3920

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

lean-workbooksource-checked

Let $a,b,c$ be positive and $a+b+c=3.$

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

Source: InternLM Lean-Workbook, record lean_workbook_3920 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3920 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 3) : a / b ^ 2 + b / c ^ 2 + c / a ^ 2 ≥ a / b + b / c + c / a  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3920; Apache-2.0

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