lean_workbook_plus_19646

Proved

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

prove that $(\forall a,b \in \mathbb{R}^{*+});(1+a^2)(1+b^2) \ge a(1+b^2)+b(1+a^2)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_19646 (a b : ℝ) (ha : 0 < a) (hb : 0 < b) : (1 + a ^ 2) * (1 + b ^ 2) ≥ a * (1 + b ^ 2) + b * (1 + a ^ 2)   :=  by sorry

Source