Prove2Me

lean_workbook_plus_8132

Proved

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

Not as nice but.. x+y+z≥xyz⟹1yz+1zx+1xy≥1 x+y+z \ge xyz \Longrightarrow \frac{1}{yz}+ \frac{1}{zx}+ \frac{1}{xy}\ge 1

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_8132 (x y z : ℝ) (hx : x > 0) (hy : y > 0) (hz : z > 0) : x + y + z >= x*y*z → 1/(x*y) + 1/(y*z) + 1/(x*z) >= 1   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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