lean_workbook_plus_80233

Proved

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

Let a,b,c follow that: \n $a+b+c>0$ \n $ab+bc+ca>0$ \n $abc>0$ \nProve that: a,b,c>0

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_80233 (a b c : ℝ) (h1 : a + b + c > 0) (h2 : a * b + b * c + c * a > 0) (h3 : a * b * c > 0) : a > 0 ∧ b > 0 ∧ c > 0   :=  by sorry

Source

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

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