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P_Product_Metric_is_Metric_v2

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

p-product-metricsproofwiki

The p-product metric on a product of metric spaces satisfies the triangle inequality.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem P_Product_Metric_is_Metric_v2 {α : Type _} {β : Type _} [MetricSpace α] [MetricSpace β] (x y z : α × β) : dist x z ≤ dist x y + dist y z := by sorry
Source
https://proofwiki.org/wiki/P-Product_Metric_is_Metric

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