A fourth-power bound under a cubic relation

Proved

WorkbookSource.plus_60066

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

lean-workbooksource-checked

Let $a,b$ be positive real numbers such that $a^3+b^3=1+ab.$ Prove that

a^4+b^4\geq a+b

Source: InternLM Lean-Workbook, record lean_workbook_plus_60066 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_60066 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) (hab : a * b > 0) (h : a^3 + b^3 = 1 + a * b) : a^4 + b^4 ≥ a + b   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_60066; Apache-2.0

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