Why isn't my PostgreSQL array index getting us

I've got a PostgreSQL array of strings as a column in a table. I created an index using the GIN method. But ANY queries won't use the index (instead, they're doing a sequential scan of the whole table with a filter). What am I missing?

Here's my migration:

class CreateDocuments < ActiveRecord::Migration
  def up
    create_table :documents do |t|
      t.string :title
      t.string :tags, array: true, default: []
      t.timestamps
    end

    add_index :documents, :tags, using: 'gin'

    (1..100000).each do |i|
      tags = []
      tags << 'even' if (i % 2) == 0
      tags << 'odd' if (i % 2) == 1
      tags << 'divisible by 3' if (i % 3) == 0
      tags << 'divisible by 4' if (i % 4) == 0
      tags << 'divisible by 5' if (i % 5) == 0

      Document.create(
        title: i,
        tags: tags
      )
    end
  end

  def down
    drop_table :documents
  end
end

Here's my query, with the resulting number of rows.

Document.where("'divisible by 5' = ANY (tags)").explain
    Document Load (249.8ms)  SELECT "documents".* FROM "documents" WHERE ('divisible by 5' = ANY (tags))
    D, [2014-03-07T17:09:49.689709 #41937] DEBUG -- :   Document Load (249.8ms)  SELECT "documents".* FROM "documents" WHERE ('divisible by 5' = ANY (tags))
    => EXPLAIN for: SELECT "documents".* FROM "documents"  WHERE ('divisible by 5' = ANY (tags))
                       QUERY PLAN
    -----------------------------------------------------------------
    Seq Scan on documents  (cost=0.00..3500.00 rows=20057 width=69)
      Filter: ('divisible by 5'::text = ANY ((tags)::text[]))
    (2 rows)

Document.where("'divisible by 5' = ANY (tags)").length
    Document Load (258.0ms)  SELECT "documents".* FROM "documents" WHERE ('divisible by 5' = ANY (tags))
    D, [2014-03-07T17:09:55.536517 #41937] DEBUG -- :   Document Load (258.0ms)  SELECT "documents".* FROM "documents" WHERE ('divisible by 5' = ANY (tags))
    => 20000

To work with a GIN index use the <@ ("is contained by") operator instead of the ANY construct.

The manual states here that default GIN indexes currently only support these operators (additional functionality is shipped with extensions):

<@
@>
=
&&

So try this query:

Document.where("'{divisible by 5}' <@ tags").explain

Note that the left hand side needs to be in array notation, too, even if it's a single element. The operator <@ works for arrays. Hence '{divisible by 5}'.