lean_workbook_plus_54261

Proved

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

Prove that if $a, b, c$ are real numbers such that $a + b + c > 0, ab + bc + ca > 0, abc > 0$ , then the numbers $a, b, c$ are positive.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_54261 (a b c : ℝ) (ha : a + b + c > 0) (hb : a * b + b * c + c * a > 0) (hc : a * b * c > 0) : a > 0 ∧ b > 0 ∧ c > 0   :=  by sorry

Source

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

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