A triple-product bound at positive sum three

Proved

WorkbookSource.plus_46670

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

lean-workbooksource-checked

If $a$ , $b$ , and $c$ are positive numbers such that $a+b+c=3$ , prove that $ab+bc+ca \geq 3abc$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_46670 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_46670 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : a * b + b * c + c * a ≥ 3 * a * b * c   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_46670; Apache-2.0

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