lean_workbook_plus_51930

Proved

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

Let $a, b, c$ be positive reals that satisfy $abc \le \frac{1}{4}$ and $\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} < 9$ . Prove that there exists a triangle with sides $a, b, c$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_51930 (a b c : ℝ) (h1 : 0 < a ∧ 0 < b ∧ 0 < c) (h2 : a * b * c ≤ 1 / 4) (h3 : 1 / a ^ 2 + 1 / b ^ 2 + 1 / c ^ 2 < 9) : ∃ a b c : ℝ, a > 0 ∧ b > 0 ∧ c > 0 ∧ a + b > c ∧ a + c > b ∧ b + c > a   :=  by sorry

Source

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

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