A mixed cubic and quartic upper bound

Proved

WorkbookSource.base_2198

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

lean-workbooksource-checked

Let $x, y > 0$ and $x^3 + y^3\leq 2$ . Prove that $x^2 + y^3 \leq x^3 + y^4+\frac{1753}{6912}$

Source: InternLM Lean-Workbook, record lean_workbook_2198 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_2198 (x y : ℝ) (hx : 0 < x) (hy : 0 < y) (h : x^3 + y^3 ≤ 2) :  x^2 + y^3 ≤ x^3 + y^4 + 1753 / 6912  :=  by sorry

Source