Database Mirroring And Log Shipping

Hello All Database Mirroring Experts,

I'm interested in how Combining Log Shipping and Database Mirroring works when failover occurs.
From SQL BOL, it says:

"Topic: Database Mirroring and Log Shipping
...
To run in high-safety mode with automatic failover the mirroring
session is configured with an additional server instance known as the witness.
If the principal database is lost for any reason after the database is
synchronized and if the mirror server and witness can still communicate
with each other, automatic failover occurs. An automatic failover
causes mirror server to assume the principal role and bring its
database online as the principal database. For more information, see Automatic Failover
[ http://msdn2.microsoft.com/en-us/library/ms189590.aspx ] . If the log
shipping backup location is accessible to the new principal/primary
server, its backup jobs begin to ship log backups to that location. The
database mirroring synchronous mode guarantees that the log chain is
unaffected by a mirroring failover and that only valid log is restored.
The secondary servers continue to copy log backups without knowing that
a different server instance has become the primary server.
..."
Source: http://msdn2.microsoft.com/en-us/library/ms187016(d=printer).aspx

Could anyone tell me that how the database mirroring synchronous mode guarantees that the log chain is
unaffected by a mirroring failover and that only valid log is restored?

Let me elaborate the situation (if anything I said is incorrect, please correct me )
Here is the time line of the failover happens:

------- tn-1 ---------- tn ---------- tf -------- tn+1 ---------------> t

----------------> t: the time line.
tn: the moment that the log shipping backup job and copy job is done for the transaction log obtained between the time interval tn-1 and tn.
tf: the moment that mirroring failover occurs in the database mirroring session.
the time interval between each tn and tn-1 are constant, say h seconds, for all n are positive integers.

Here is the question that I want to ask:
In database mirroring synchronous mode, it guarantees that all the committed transaction from the moment tn to tf is copied to the mirror database. All the transaction log backup for log shipping are done on the original principal before the moment tf. After the mirroring failover occurs at the moment tf, how the log shipping mechanism guarantees that the transaction log between the interval tn and tn+1 that can be unaffected by a mirroring failover?
That's the point that I interested in.

Thanks a lot,
Terence