They didn't prove anything, we or PSG are going to sign him next year for less.
Yes, they did and even if he leaves next summer won't change that fact.
They did not manage to replace him in this transfer window and therefore refused to sell him, no matter if they sell him for less next summer (which I somehow doubt, as PSG could easily again make some huge transfer, plus if Brazil keeps playing like this and he makes a great World Cup, his price could even go higher).
Next summer, when Liverpool have time to get his replacement (already got Keita by the way) and if he continues to show he does not want to play for them, then they could sell him, but the difference is that this time it won't be just like previous years, the moment the player wants to leave he does - this time they would already have a replacement for him and they would have already shown that they are an ambitious club that did not bend the second he wanted to leave, just to take the money.
At least I see it that way.
And of course all my words could mean absolutely nothing if they sell him today, but I think I could handle that