What is an easy query to fix up historical columns valid_from and valid_to?

I have a table with typical history rows using valid_from and valid_to dates. My table might look like this:

| id | object_id | name | valid_from | valid_to
--------------------------------------------------
|  1 | 1000      | Foo  | 2010-07-01 |   null
|  2 | 1000      | Bar  | 2011-12-31 |   null
|  3 | 2000      | Baz  | 2010-08-04 |   null
|  4 | 2000      | Bang | 2013-03-21 |   null

I’d like run a SQL update such that it would update valid_to of a row to next historical valid_from date minus 1 day if possible. So therefore the table might look like this when the query is done:

| id | object_id | name | valid_from | valid_to
--------------------------------------------------
|  1 | 1000      | Foo  | 2010-07-01 |   2011-12-30
|  2 | 1000      | Bar  | 2011-12-31 |   null
|  3 | 2000      | Baz  | 2010-08-04 |   2013-03-20
|  4 | 2000      | Bang | 2013-03-21 |   null

I’ve tried a few different variations, but I’m striking out on this one:

select * 
from employees as cur 
where cur.valid_from < (
    select nx.valid_from from employees as nx 
    where 
       cur.source_id=nx.source_id 
       and nx.valid_from > cur.valid_from
);

And

update employees cur 
set cur.valid_to = (
    select nx.valid_from 
    from employees nx 
    where cur.source_id=nx.source_id 
          and nx.valid_from > cur.valid_from
);

Part of the problem with the subquery as I’ve written it is that it will return multiple rows. I just need the very first row that occurs after the valid_from of the current row. And the update statement MySQL complains that cur.valid_from cannot be used in the subquery.

I’m trying to find a query that would be portable between Oracle and MySQL. Can someone get me on the right track?