lean_workbook_plus_29329

Proved

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

The function: $f(t) = {t^5}$ is convex in $[0, + \infty )$ , so: $\forall \mathop {}\limits^{} x,y \in [0, + \infty )$ , $f\left( {\frac{{x + y}}{2}} \right) \le \frac{{f(x) + f(y)}}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_29329  (x y : ℝ)
  (h₀ : 0 ≤ x ∧ 0 ≤ y) :
  ((x + y) / 2)^5 ≤ (x^5 + y^5) / 2   :=  by sorry

Source

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

View graph