Four positive reciprocals sum to at least sixteen divided by the total

Proved

WorkbookSource.base_33098

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

lean-workbooksource-checked

Prove that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}+\frac{1}{d}\ge\frac{16}{a+b+c+d}$ for all positive $a, b, c$ and $d$ .

Source: InternLM Lean-Workbook, record lean_workbook_33098 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_33098 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (1 / a + 1 / b + 1 / c + 1 / d) ≥ 16 / (a + b + c + d)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_33098; Apache-2.0

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