lean_workbook_plus_61819

Proved

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

Let $a,b,c$ be positive real numbers such that $abc=1$ . Then prove that \n $(a^2+1)(b^2+1)(c^2+1)\ge (a+1)(b+1)(c+1).$ \n

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_61819 (a b c : ℝ) (habc : a * b * c = 1) :  (a^2 + 1) * (b^2 + 1) * (c^2 + 1) ≥ (a + 1) * (b + 1) * (c + 1)   :=  by sorry

Source