A reciprocal sum bounds mixed quadratic reciprocals

Proved

WorkbookSource.base_25312

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

lean-workbooksource-checked

Let $a,b,c>0$ , prove that: $\sum{\frac{1}{a}}\geq\sum{\frac{3a}{a^2+2bc}}$

Source: InternLM Lean-Workbook, record lean_workbook_25312 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_25312 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / a + 1 / b + 1 / c ≥ 3 * a / (a ^ 2 + 2 * b * c) + 3 * b / (b ^ 2 + 2 * c * a) + 3 * c / (c ^ 2 + 2 * a * b)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_25312; Apache-2.0

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