... if I can prove I have 10BTC then I could invest that 10BTC ...
How would this investment work without those coins leaving your wallet?
I might have to be restricted from spending the BTC during that time, but I could still own it myself.
If you own them (they are in a wallet you control) who will how prevent you from spending?
The investor would be able to use the BTC to invest, but I would still own it.
e.g. You put your coins to a trading place. The trader does some arbitrage gambling. ... things happen or not ...
Ok you might say I still own them while I can´t spend them.
Yes, that much is true. But how do you get your coins back? You have to trust the trader being a nice guy.
... and there would be a system in place to guarentee this?
Has anybody been to court with Bitcoins yet?
The investor could then show others proof of the BTC existance but not actually give them the BTC.http://blockexplorer.com/
Here you can see existing Bitcoins without anybody actually giving them to you.