lean_workbook_plus_49072

Proved

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

Let $a,b,c>0$ . By Cauchy-Schwarz inequality, $(a+b+c)^2 \leq 3(a^2+b^2+c^2)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_49072 : ∀ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 → (a + b + c) ^ 2 ≤ 3 * (a ^ 2 + b ^ 2 + c ^ 2)   :=  by sorry

Source