lean_workbook_plus_64700

Proved

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

Prove the lemma: If $x,y,z \in \mathbb{R}$ such that $x+y+z>0, xy+xz+yz>0, xyz>0$ , then $x,y,z>0$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_64700 (x y z : ℝ) (hx : x + y + z > 0) (hy : x*y + x*z + y*z > 0) (hz : x*y*z > 0) : x > 0 ∧ y > 0 ∧ z > 0   :=  by sorry

Source