lean_workbook_plus_15509

Proved

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

Prove that $a^2 + b^2 + c^2 \ge 3$ if $a, b, c > 0$ and $a + b + c \ge 3$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_15509 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c >= 3) : a^2 + b^2 + c^2 >= 3   :=  by sorry

Source