lean_workbook_plus_478

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Let $a,b,c,d$ be non-negative real numbers such that $a^{3}+b^{3}+c^{3}+d^3 \le d^2$ . Show that $a^4+b^4+c^4+d^4\ge{d^5}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_478 {a b c d : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) (hc : 0 ≤ c) (hd : 0 ≤ d) (habc : a * b * c = 1) (h : a^3 + b^3 + c^3 + d^3 ≤ d^2) : a^4 + b^4 + c^4 + d^4 ≥ d^5   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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