lean_workbook_plus_57185

Proved

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

prove that if a,b,c are positive numbers satisfying $abc\le \frac{1}{4}$ and $\frac{1}{a^{2}}+\frac{1}{b^{2}}+\frac{1}{c^{2}}<9$ then there exists a triangle with sides a,b,c.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_57185 (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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