A reciprocal sum lower bound at fixed sum six

Proved

WorkbookSource.base_49525

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

lean-workbooksource-checked

Let $a,b,c$ be positive real numbers having sum $6.$ Prove that $\frac {1}{a} + \frac {1}{b} + \frac {1}{c} \ge \frac {21}{abc + 6}.$

Source: InternLM Lean-Workbook, record lean_workbook_49525 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_49525 (a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (habc : a + b + c = 6) : 1 / a + 1 / b + 1 / c ≥ 21 / (a * b * c + 6)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_49525; Apache-2.0

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