lean_workbook_plus_57415

Proved

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

Let $x,y,z$ be nonzero real numbers such that $x+y+z=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1$ . Prove that at least one of $x,y,z$ is equal to 1.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57415 (x y z : ℝ) (hx : x ≠ 0) (hy : y ≠ 0) (hz : z ≠ 0) (hxy : x + y + z = 1) (h : 1/x + 1/y + 1/z = 1) : x = 1 ∨ y = 1 ∨ z = 1   :=  by sorry

Source

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

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