I am reading Flink 1.20 doc at https://nightlies.apache.org/flink/flink-docs-release-1.20/docs/dev/table/sql/queries/joins/#processing-time-temporal-join

It is said that it doesn’t support processing time temporal join using `the FOR SYSTEM_TIME AS OF syntax currently and should use LATERAL TABLE to temporal join

Currently, the FOR SYSTEM_TIME AS OF syntax used in temporal join with
latest version of any view/table is not support yet, you can use
temporal table function syntax as following:

SELECT
  o_amount, r_rate
FROM
  Orders,
  LATERAL TABLE (Rates(o_proctime))
WHERE
  r_currency = o_currency
 

But, in the lookup join section (https://nightlies.apache.org/flink/flink-docs-release-1.20/docs/dev/table/sql/queries/joins/#lookup-join), it is using the FOR SYSTEM_TIME AS OF syntax

-- Customers is backed by the JDBC connector and can be used for lookup joins
CREATE TEMPORARY TABLE Customers (
  id INT,
  name STRING,
  country STRING,
  zip STRING
) WITH (
  'connector' = 'jdbc',
  'url' = 'jdbc:mysql://mysqlhost:3306/customerdb',
  'table-name' = 'customers'
);

-- enrich each order with customer information
SELECT o.order_id, o.total, c.country, c.zip
FROM Orders AS o
  JOIN Customers FOR SYSTEM_TIME AS OF o.proc_time AS c
    ON o.customer_id = c.id;

In the above, processing time temporal join says it it not supporting FOR SYSTEM_TIME AS OF syntax used in temporal join, while in the lookup join section it is using processing-time-temporal-join syntax?

So, whether FOR SYSTEM_TIME AS OF syntax used in temporal join is supported or not, completely confused.