A reciprocal sum involving a pair sum and product is at least two

Proved

WorkbookSource.plus_74668

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

lean-workbooksource-checked

Let $a,b,c>0$ and $a+b+c=3 .$ Prove that

\frac{1}{a+b }+\frac{1}{(a+b)c }+\frac{1}{a bc} \geq 2

Source: InternLM Lean-Workbook, record lean_workbook_plus_74668 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_74668 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hab : a + b + c = 3) : 1 / (a + b) + 1 / ((a + b) * c) + 1 / (a * b * c) ≥ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_74668; Apache-2.0

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