A reciprocal sum with a triple-product correction

Proved

WorkbookSource.base_17854

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers such that $a+b+c=3$ . Prove that $\frac{1}{a}+ \frac{1}{b}+ \frac{1}{c}+ \frac{3}{2}abc\ge \frac{9}{2}.$

Source: InternLM Lean-Workbook, record lean_workbook_17854 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_17854 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 3) : 1 / a + 1 / b + 1 / c + 3 / 2 * a * b * c ≥ 9 / 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_17854; Apache-2.0

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