lean_workbook_plus_37135

Proved

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

Let $a,b, c>0$ . $(a^2+1)(b^2+1)(c^2+1) \geqslant \dfrac{5}{16}(ab+bc+ca+1)^2$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_37135 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ (5/16) * (a * b + b * c + c * a + 1)^2   :=  by sorry

Source

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

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