lean_workbook_plus_32906

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

If $a, b, c, d$ are real positives that satisfy: $a + b + c + d = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d}$ .\nProve that $ab + ac + ad + bc + bd + cd \geq 6abcd$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_32906 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) (hab : a + b + c + d = 1 / a + 1 / b + 1 / c + 1 / d) : a * b + a * c + a * d + b * c + b * d + c * d ≥ 6 * a * b * c * d   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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