Is this the correct way to create SQL assertion?

in order to make the following type of assertion

create assertion assert  
check "EMPTY SET" = (select User         
     from Video  
     where date=current_date()  
     group by user  
having count(*) >= 10

is this assertion right?

create assertion assert  
check  0 = (select count(*)  
     from Video  
     where date=current_date()  
     group by user  
having count(*) >= 10

For full details on CREATE ASSERTION see the ISO SQL-92 Standard spec.

The CHECK definition should be in parentheses.

CURRENT_DATE does not have parentheses.

USER and DATE are reserved words.

SQL statements should be terminated with a semicolon character.

SQL Keywords should be in upper case.

Try something more like this:

CREATE ASSERTION assert  
CHECK (0 = (
            SELECT COUNT(*)  
              FROM Video  
             WHERE my_date = CURRENT_DATE  
             GROUP 
                BY my_user
            HAVING COUNT(*) >= 10
           ));

You can test that the syntax is correct using the online Mimer SQL-92 Validator. However, you should also test your logic e.g. CURRENT_DATE is non-deterministic.

Also, I don't think this ASSERTION will ever bite. When the cardinality of the subquery is less than 10 it will return zero rows and 0 = empty set will evaluate to UNKNOWN. When the cardinality of the subquery is 10 or greater then the search condition will evaluate TRUE. SQL-92 Standard states

The assertion is not satisfied if and only if the result of evaluating the search condition is false.

Note you can replace your CHECK (0 = (SELECT COUNT(*) FROM...)) construct with CHECK (NOT EXISTS (SELECT * FROM...)), the latter of which I find easier to write.

UPDATE:

How should I write the assertion using CHECK NOT EXISTS ?

As I said above, your logic appears flawed so it is hard to implement properly ;)

Let's say the rule is to limit Videos to 10 per user per day. Because this involves only a single table, it would be more appropriate to use a table-level CHECK constraint; such a constraint is checked when the table is updated which is sufficient in this case (there's no reason why it couldn't be an ASSERTION, though, which in theory could be checked each time any table in the schema is updated):

ALTER TABLE Video ADD 
   CONSTRAINT video_limit_10_per_user_per_day
      CHECK (NOT EXISTS (
                         SELECT v1.my_user, v1.my_date
                           FROM Video AS V1
                          GROUP BY v1.my_user, v1.my_date
                         HAVING COUNT(*) > 10
                        ));

UPDATE 2:

thanks,now let's say we want to limit videos to 100 per user per year, in this case using current_date would be necessary wouldn't it?

Consider again that a CHECK/ASSERTION will only be checked when data in the table/schema is updated. The problem with using CURRENT_DATE (and other non-determninistic functions) in a constraint is that the business rule can be invalidated simply by the clock ticking over from one time period to the next but if the data hasn't been changed in that period then the data integrity failure will not be detected and the database will contain invalid data.

Another consideration is what is meant by a year in context.

It could be the calendar year (1 Jan to 31 Dec inclusive) or other other fixed dates defined by enterprise (e.g. 1 Apr to 31 Mar inclusive), in which case grouping by year and user then counting is trivial.

A more interesting case is when the rule limits the tally for any 12 month period; extending this to both the past and future avoid the above 'non-deterministic' issue.

Consider a standard approach of using an auxiliary calendar table, containing one row for every day applicable to the enterprise, extended into the past and future only as far as required should still only comprise a few thousand rows. Each row would have the date as a key with a second column for that date plus one year (and if necessary you could fine tune the definition of 'a year' at one-day granularity!) The test for would involve joining to the Calendar table, grouping on the calendar date and user and counting e.g. something like this:

SELECT C1.dt, V1.my_user
  FROM Video AS V1
       INNER JOIN Calendar AS C1
          ON (V1.my_date BETWEEN C1.dt AND C1.dt_plus_one_year)
 GROUP 
    BY C1.dt, V1.my_user
HAVING COUNT(*) > 100;

This could be put in a CHECK (NOT EXISTS (... constraint. This could still be a table-level CHECK constraint: because the Calendar table is an auxiliary table it would only be suject to infrequent controlled updates (but again could be an ASSERTION if required).