lean_workbook_plus_3092

Proved

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

Let $a, b, c > 0$ such that $a \geq 3$ , $\frac{a}{3} + \frac{b}{2} \geq 2$ , and $\frac{a}{3} + \frac{b}{2} + c \geq 3$ . Prove that $a^3 + b^3 + c^3 \geq 36$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_3092 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a ≥ 3) (hbc : a / 3 + b / 2 ≥ 2) (habc : a / 3 + b / 2 + c ≥ 3) : a ^ 3 + b ^ 3 + c ^ 3 ≥ 36   :=  by sorry

Source

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

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