lean_workbook_plus_9906

Proved

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

Let $a,b,c \ge 0$ such that $a+b+c=1$ . Prove that \n

a^2+b^2+c^2 \le \frac{1}{4}+a^3+b^3+c^3

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9906 (a b c : ℝ) (ha : a ≥ 0 ∧ b ≥ 0 ∧ c ≥ 0) (hab : a + b + c = 1) : a^2 + b^2 + c^2 ≤ 1 / 4 + a^3 + b^3 + c^3   :=  by sorry

Source

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

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