lean_workbook_plus_19714

Proved

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

Prove $ab+bc+ac>0$ and $\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ac}>0$ if $a, b, c$ have the same sign.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19714 (a b c : ℝ) (hab : a * b > 0) (hbc : b * c > 0) (hca : a * c > 0) : a * b + b * c + a * c > 0 ∧ 1 / (a * b) + 1 / (b * c) + 1 / (a * c) > 0   :=  by sorry

Source

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

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