A cubic sum bound under a sum-product relation

Proved

WorkbookSource.plus_73118

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Let $a,b,c\geq 0$ and $a+b+c= abc+3.$ Prove that

a^3+b^3+c^3\geq \frac{27}{4}

Source: InternLM Lean-Workbook, record lean_workbook_plus_73118 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_73118 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c = a * b * c + 3) : a ^ 3 + b ^ 3 + c ^ 3 ≥ 27 / 4   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_73118; Apache-2.0

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