lean_workbook_plus_9202

Proved

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

If $a,b,c,d\geq -1.$ Prove that $a^3+b^3+c^3+d^3\ge\frac{3}{4}(a+b+c+d)-1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_9202 (a b c d : ℝ) (hab : a ≥ -1) (hbc : b ≥ -1) (hcd : c ≥ -1) (hda : d ≥ -1) : a^3 + b^3 + c^3 + d^3 ≥ (3/4 : ℝ) * (a + b + c + d) - 1   :=  by sorry

Source

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

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