A triple product with a symmetric reciprocal correction

Proved

WorkbookSource.base_46263

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

lean-workbooksource-checked

Let $a,b,c>0$ , s.t. $a+b+c=3$ .Prove that: $abc+\frac{12}{ab+bc+ca}\geq 5$

Source: InternLM Lean-Workbook, record lean_workbook_46263 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_46263 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (habc : a + b + c = 3) : a * b * c + 12 / (a * b + b * c + c * a) ≥ 5  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_46263; Apache-2.0

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