Prove2Me

lean_workbook_plus_14146

Disproved

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

The following inequality is true: 1(a+1)2+1(b+1)2+1(c+1)2+ab+bc+ca8≥98\frac{1}{{{{\left( {a + 1} \right)}^2}}} + \frac{1}{{{{\left( {b + 1} \right)}^2}}} + \frac{1}{{{{\left( {c + 1} \right)}^2}}} + \frac{{ab + bc + ca}}{8} \ge \frac{9}{8}.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_14146 : ∀ a b c : ℝ, (1 / (a + 1) ^ 2 + 1 / (b + 1) ^ 2 + 1 / (c + 1) ^ 2 + (a * b + b * c + c * a) / 8) ≥ 9 / 8   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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