Use of 'A' vs. 'The'?

[khaledwawa]

Hello.
The rule states that: Use (A) the first time you mention something, and (The) the second time you mention the same thing.
Kindly, consider the following example: (source: English for Starters 9)
((I'm going to tell you about a city called Tripoli, in the north of Lebanon. It is a city with lots of beautiful old houses.))
My question is:
According to the rule, we should say:
((It is the city with lots of beautiful old houses)), because it is the second time we mention the word (city).
Why did we use (a) instead of (the) in this situation?
Thanks in advance.

[Alan]

For defintions/general descriptions we always use the indefinite article.

(The definite article in this position would be absurd, suggesting that Tripoli is the ONLY city with lots of beautiful old houses!)