Is there Such Thing As The Opposite of Unique Constraint I want to be constrain my database with what is essentially the opposite of a UNIQUE constraint. I want to only be able to add a new row if some combination of fields has been added before. 

Note: I am working within postgres.

Take the following datasets for example. I want a "NON UNIQUE" constraint on the following:

1, a, 1

1, a, 1

1, b, 1


I should not have been able to add the row (1, b, 1) since it has not appeared before. There are also other fields I don't want to constrain so it's not like all the entries are identical.

This may be a separate question, but I would also like to add the constraint that all rows with the same value in one column (i.e. a in the above example) have the same value in another. 

So I want this to be impossible

1, a, 1

1, a, 1

0, a, 1


But this is ok

1, a, 1

1, a, 1

0, b, 1


I have looked around pretty heavily and the opposite of this is possible
with unique constraints, but I can't find anything that works for this.
Check constraints will only look at the row in question, and won't take into account the entire table's entries like a unique constraint would.

Is this even possible? Or is this now out of the realms of Postgres functionality, and must be done in-application.
Subqueries are not allowed in a CHECK constraint, or in the WHEN clause of a trigger, but you can use them inside a trigger function, something like this:

CREATE FUNCTION my_little_trigger_function()
RETURNS TRIGGER
AS $$
DECLARE
   row_count int;
BEGIN
   row_count := (SELECT COUNT(*)
                 FROM ...
                 WHERE ... = NEW.x ...);
   IF (row_count = 0) THEN
       RAISE EXCEPTION 'I''m sorry, Dave. I''m afraid I can''t do that.';
   END IF;
   RETURN NEW;
END
$$ LANGUAGE plpgsql;

CREATE TRIGGER my_little_trigger
BEFORE INSERT ON my_little_table
FOR EACH ROW
EXECUTE PROCEDURE my_little_trigger_function();