A shifted reciprocal sum bounds a symmetric rational expression

Proved

WorkbookSource.base_18063

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

lean-workbooksource-checked

prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+2 \ge \frac{12+3abc}{ab+bc+ca}$ given $a,b,c > 0$ and $a+b+c=3$

Source: InternLM Lean-Workbook, record lean_workbook_18063 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_18063 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b + c = 3) : 1 / a + 1 / b + 1 / c + 2 ≥ (12 + 3 * a * b * c) / (a * b + b * c + c * a)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18063; Apache-2.0

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