lean_workbook_plus_78737

Proved

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

Let $a,b,c>0$ and $ab+bc+ca+abc=4 .$ prove that

a^3+b^3+c^3+abc\geq 4

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78737 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a * b + b * c + c * a + a * b * c = 4) : a ^ 3 + b ^ 3 + c ^ 3 + a * b * c ≥ 4   :=  by sorry

Source

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

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