lean_workbook_plus_68662

Proved

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

Prove that for any positive real numbers $a, b, c$ , the following inequality holds: $\\sqrt{a^2+b^2}+\\sqrt{b^2+c^2}+\\sqrt{c^2+a^2} \\geq a+b+c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_68662 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) : √(a^2 + b^2) + √(b^2 + c^2) + √(c^2 + a^2) ≥ a + b + c   :=  by sorry

Source

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

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