Transaction ordering on log-shipping standby

I've got a question about transaction ordering in a log-shipping replication environment.

Here's the setup...

- A pair of PostgreSQL 9 servers in active/standby configuration, using log-shipping
- A single client, using a single connection
- The client commits transaction 1
- The client commits transaction 2
- The active server fails and the standby is promoted to be the active server

The client re-establishes the connection and is attempting to determine which transactions have made it onto the standby server (and which never made it because of replication delays).

Here's the question...

If the client can confirm that transaction 2 has happened on the standby, does that imply that transaction 1 has also made it onto the standby?

Or to put the question another way, is the ordering of transactions on the active and standby servers guaranteed to be the same?

Thanks,

Andrew