lean_workbook_plus_78633

Proved

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

$x_ix_{i+1} \leq \frac{{x_i}^2+{x_{i+1}}^2}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_78633 (x : ℕ → ℝ) (i : ℕ) : x i * x (i + 1) ≤ (x i ^ 2 + x (i + 1) ^ 2) / 2   :=  by sorry

Source