A cubic bound under a mixed sum constraint

Proved

WorkbookSource.base_3158

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

lean-workbooksource-checked

Let $a,b,c$ be non negative reals such that $a+b+c+ab+bc+ca=6$ . Prove that $4(a+b+c)+abc\ge\ 13.$

Source: InternLM Lean-Workbook, record lean_workbook_3158 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_3158 (a b c : ℝ) (ha : a ≥ 0) (hb : b ≥ 0) (hc : c ≥ 0) (habc : a + b + c + a * b + b * c + c * a = 6) : 4 * (a + b + c) + a * b * c ≥ 13  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_3158; Apache-2.0

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