An inequality with powers two, four and eight

Proved

WorkbookSource.plus_62169

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

lean-workbooksource-checked

Let $a$ , $b$ , $c$ and $d$ be real positive numbers. Prove that: $4a^2 + 2b^4 + c^8 + d^8 \geq 8abcd$

Source: InternLM Lean-Workbook, record lean_workbook_plus_62169 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.plus_62169 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : 4 * a ^ 2 + 2 * b ^ 4 + c ^ 8 + d ^ 8 ≥ 8 * a * b * c * d   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_62169; Apache-2.0

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