Averages of initial segments of a nondecreasing sequence

Proved

WorkbookSource.problem_9858

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove that $\frac{x_{1}+x_{2}+\cdots+x_{6}}{6} \leq \frac{x_{1}+x_{2}+\cdots+x_{10}}{10}$ for $x_{1} \leq x_{2} \leq \cdots \leq x_{10}$ .

Source: InternLM Lean-Workbook, record lean_workbook_9858 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_9858 (x : ℕ → ℝ) (hx : Monotone x) : (x 1 + x 2 + x 3 + x 4 + x 5 + x 6) / 6 ≤ (x 1 + x 2 + x 3 + x 4 + x 5 + x 6 + x 7 + x 8 + x 9 + x 10) / 10  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9858; Apache-2.0

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