A cyclic quadratic ratio sum bounds shifted pairwise squares

Proved

WorkbookSource.base_5148

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

lean-workbooksource-checked

הוכיחו כי עבור $a>0 , b>0 , c>0$ מתקיים: $\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{a} \ge \frac{\frac{(a+c)^2}{b+c}+\frac{(b+a)^2}{c+a}+\frac{(c+b)^2}{a+b}}{2}$

Source: InternLM Lean-Workbook, record lean_workbook_5148 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_5148 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 / b + b^2 / c + c^2 / a) ≥ (1 / 2) * ((a + c) ^ 2 / (b + c) + (b + a) ^ 2 / (c + a) + (c + b) ^ 2 / (a + b))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_5148; Apache-2.0

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