Lean-Workbook Plus 17667: Logarithmic inequality

Proved

WorkbookRestored.plus_17667

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

Prove that $x^4y^4\ge x^3y^3+\ln(xy)\quad\forall x,y>0$

Source: Lean-Workbook row lean_workbook_plus_17667 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

import Mathlib.Analysis.SpecialFunctions.Log.Basic
open Real

Formal statement

theorem WorkbookRestored.plus_17667 : ∀ x y : ℝ, x > 0 ∧ y > 0 → x^4*y^4 ≥ x^3*y^3 + Real.log (x*y)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_17667; immutable original Prove2Me node 472d5ad5-8e82-4698-84a2-1c70c0c0d080

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