lean_workbook_plus_31796

Proved

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

We have that $ab*\frac{a}{b}=a^2>0$ so $ab$ and $\frac{a}{b}$ have the same sign.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_31796  (a b : ℝ)
  (h₀ : b ≠ 0)
  (h₁ : a * b * (a / b) > 0) :
  a^2 > 0   :=  by sorry

Source