A mixed polynomial bound on a simplex

Proved

WorkbookSource.problem_49227

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a, b, c\geq 0$ and $a+b+c=3$ . Then

3a^2+3b^2+c^3\leq 27

Source: InternLM Lean-Workbook, record lean_workbook_49227 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_49227 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c = 3) : 3 * a ^ 2 + 3 * b ^ 2 + c ^ 3 ≤ 27  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_49227; Apache-2.0

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