A mixed square and cubic bound under a nonlinear sum constraint

Proved

WorkbookSource.base_50900

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $x$ , $y$ and $z$ be non-negative numbers such that $x+y+z\geq x^2+y^3+z^3$ . Prove that $3x^2+4y^3+4z^3\leq 11$

Source: InternLM Lean-Workbook, record lean_workbook_50900 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_50900 (x y z : ℝ) (hx : 0 ≤ x) (hy : 0 ≤ y) (hz : 0 ≤ z) (h : x + y + z ≥ x^2 + y^3 + z^3) : 3 * x^2 + 4 * y^3 + 4 * z^3 ≤ 11  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_50900; Apache-2.0

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