lean_workbook_plus_67106

Proved

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

Prove that $1\leq x+y+z+xyz\leq 2$ for $0<x,y,z<1$ such that $xy+yz+zx=1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_67106 (x y z : ℝ) (hx : 0 < x ∧ x < 1) (hy : 0 < y ∧ y < 1) (hz : 0 < z ∧ z < 1) (h : x * y + y * z + z * x = 1) : 1 ≤ x + y + z + x * y * z ∧ x + y + z + x * y * z ≤ 2   :=  by sorry

Source

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

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