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Finite_Subset_of_Metric_Space_has_no_Limit_Points

Proved

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

metric-spacesproofwiki

Let M = (A, d) be a metric space. Let X be a finite subset of A. Then X has no limit points.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem Finite_Subset_of_Metric_Space_has_no_Limit_Points {X : Type _} [MetricSpace X] {S : Set X} (hS : Set.Finite S) (x : X) (hx : x ∈ closure S) (hx2 : x ∉ S) : False := by sorry
Source
https://proofwiki.org/wiki/Finite_Subset_of_Metric_Space_has_no_Limit_Points

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