What should I do to prove that I'm not into my ex anymore?

STAY THE HELL AWAY FROM THE EX! God! It's so stupid how people have to interact with their ex when they're into someone new. And never talk about her to your new girl, no matter what you say we will believe you are not over her. You may cross paths but that's not an invitation to be around her and hang with her. Exes are evil creatures that need to go away. As for the new girl, call her, talk to her a lot, show her you're interested in her and only her without being too pushy. Ask her out already!

Just because you cross paths with someone daily does not mean you have to converse with them. If you like this other girl then show her by not speaking to the ex every chance you get. I'm not saying totally ignore her but at least when this girl is around. From now on though I wouldn't go into to much detail about previous relationships to whomever you are crushing on some girls may ask but usually don't want to know every detail.

Hang around this girl you like 10 times more than your ex. Don't totally ignore your ex. Ask some of this girls friends about her and show a lot of interest in her. After about 2 weeks ask her out.

Well. I had the same problem. I hate exs. No offense! But what you can do is. Try not talking to your ex while seeing the girl you like! Pretend like you don't see your ex. Don't greet her with a kiss on the cheek or a hug. Don't do that please! Its really stupid when exs do that! Avoid your ex. That way the girl you like will know you're over your ex. The less talking the better!