lean_workbook_plus_1255

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let a, b, c be three positive real numbers such that $a+b+c=3$ . Prove that $\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} \ge \frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_1255 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 3) : (1 / a ^ 2 + 1 / b ^ 2 + 1 / c ^ 2) ≥ (1 / (a * b) + 1 / (b * c) + 1 / (c * a))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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