Cookham Library (Q55114757)

• matcher place: Berkshire (relation 88070), Royal Borough of Windsor and Maidenhead (relation 111014)
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  [timeout:300][out:json];
  (
      node(around:1000,51.55650,-0.72740)[amenity=library][~"^(addr:housenumber|.*name.*)$"~".",i];
      way(around:1000,51.55650,-0.72740)[amenity=library][~"^(addr:housenumber|.*name.*)$"~".",i];
      rel(around:1000,51.55650,-0.72740)[amenity=library][~"^(addr:housenumber|.*name.*)$"~".",i];
      node(around:1000,51.55650,-0.72740)[government=culture][~"^(addr:housenumber|.*name.*)$"~".",i];
      way(around:1000,51.55650,-0.72740)[government=culture][~"^(addr:housenumber|.*name.*)$"~".",i];
      rel(around:1000,51.55650,-0.72740)[government=culture][~"^(addr:housenumber|.*name.*)$"~".",i];
  );
  out center tags;

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found a single match candidate

Search criteria from Wikidata

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cultural institution (Q3152824)	government=culture
library (Q7075)	amenity=library