Does this example phrase fit in here?

Question

Using an online translator to translate "Then it can be demonstrated that the statement is true."

I get "Entonces se puede demostrar que la afirmación es verdadera."

In the English translation it is optional whether you say "it can be demonstrated" or "one can demonstrate".

Is this the same construct as the one covered in this lesson? If so, should there be examples of it above? If not, is there a lesson that covers this one?

Thank you!

Accepted Answer

Hola Gabor
The sentence you are showing:
"Entonces se puede demostrar que la afirmación es verdadera."
is not an impersonal sentence, it is a passive using "se" .
In the lesson we are explaining how this structure "se puede + infinitive" is a type of impersonal sentence, but for that, it needs verbs that are intransitive (no direct objects).
Here you have a direct object in the form of a subordinate clause:
"que la afirmación es verdadera".
Imagine that we substitute that clause with "algo", so we'd say:
"Entonces se puede demostrar algo"
You can turn this into a passive sentence saying:
Entonces algo puede ser demostrado. 
This is what you got with that translation: 
"Then it can be demonstrated that the statement is true."
However, sometimes, and to make it sound more natural, you can see a translation using an impersonal form: "Then one can demonstrate..." (this is not passive)
In the lesson you saw, if you go to the bottom, you find a link to another lesson on this same structure but using "se puede/n + infinitive". That lesson is about this same struccture but being passive sentences. Here you can use the plural when you have a plural object. For example:
Entonces se pueden demostrar dos cosas.
This is another passive "se" sentence. The verb needs agreement with the object (dos cosas)
I hope this clarifes it a bit. Just so you know, this is a topic (impersonal vs passive se) where not all grammarians agree, so it's always a "noisy" topic. 
Saludos
Inma