Prove2Me

A weighted quadratic cyclic ratio difference is nonnegative

Proved
WorkbookSource.base_13321

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

lean-workbooksource-checked

Let a,b,c be positive real numbers. Prove that: (a2+2b2)(ac−1)+(b2+2c2)(ba−1)+(c2+2a2)(cb−1)≥0 (a^{2}+2b^{2})(\frac{a}{c}-1)+(b^{2}+2c^{2})(\frac{b}{a}-1)+(c^{2}+2a^{2})(\frac{c}{b}-1)\ge 0

Source: InternLM Lean-Workbook, record lean_workbook_13321 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.base_13321 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) :  (a^2 + 2 * b^2) * (a / c - 1) + (b^2 + 2 * c^2) * (b / a - 1) + (c^2 + 2 * a^2) * (c / b - 1) ≥ 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_13321; Apache-2.0

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