Prove2Me

lean_workbook_plus_848

Proved

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

Prove the generalized triangle inequality: of x1,x2,⋅,xnx_1, x_2, \cdot, x_n are real numbers, then

∣x1+x2+⋯+xn∣≤∣x1∣+∣x2∣+⋯+∣xn∣.|x_1+x_2+\cdots +x_n| \leq |x_1| + |x_2| + \cdots + |x_n|.
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_848 (n : ℕ) (x : Fin n → ℝ) : 
  |∑ i, x i| ≤ ∑ i, |x i|   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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