No, not in addition, instead. MATE is found only in the regular version of
Trisquel, not in Trisquel-Mini.
> The question came to me about why the default desktop will not be deleted.
Are you talking about the Trisquel-Mini entry in the display manager (login
screen)? If you're still seeing that, it would be because you haven't removed
the package that provides it.
What do you get with this command?
aptitude search "~i trisquel"
> Given that Trisquel is a completely free operating system, so I must have
the right to remove softwares that I don't need them.
Please don't insinuate that Trisquel is forcing you to keep packages
installed. It doesn't have the power to do that, nor does it try to. If you
still see something you have no use for, that's just because you haven't
removed the package that provides it.
If you're so concerned about having an environment with no trace of LXDE or
Trisquel-Mini, you went about your installation the wrong way. Rather than
installing these things and then hunting down what packages to remove, you
should have done a net-install and not installed trisquel-mini to begin with.
But nothing is stopping you from hunting down the package that is providing
whatever it is that you don't need. Or just deleting the files, even.
