An application

This is a discussion in a passport bureau where English is spoken officially.


We're talking about passport applications. Someone is training us on them.


"Let's say someone fills out an application incorrectly. In that case . . ."

"Let's look at another example. An individual filled out an application correctly, but forgot to pay. What do we do? . . ."

He continues:

"Let's say it takes someone more than a month to submit an application. The application is late. In that case . . ."


I am using "an" before "application" in each sentence, because as the speaker moves from one example to others, he introduces the application again with each one. Is the "an" correct?