Could somebody be traced in a situation like this? I'm fairly new to bitcoins and wanted to know if somebody could be traced easily in a situation like this:


Somebody buys btc with his/her own name
Btc are sent to an address, an offline wallet, which already has some bitcoins in it. The wallet is not associated with his/her name, other than the fact that the btc the specific somebody bought are sent to that wallet.
He/she sends all of the bitcoins from that wallet trough a mixing service via tor to some address.


There is one condition. It is known that he/she bought the bitcoins and had them sent to the address of that offline wallet.

More specifically: could it be proven that that somebody who bought the coins and had them sent to the offline wallet was the one who sent all of the wallet's coins to the final address?
Bitcoin addresses are pseudonymous, in other words they aren't linked to anybody's ID without that user somehow linking the address to their ID (for example by withdrawing from an exchange service where they have provided their ID to the exchange). 

There are various known tricks/tools to reveal IP addresses of transactions and to link various addresses to a wallet if they are all in the same actual wallet. Each have varying degrees of success. But at the end of the day if an address is used only once and isn't part of a wallet with other addresses in it, plus you use tools like Tor and mixing services it would be very difficult to link future addresses to the source address while still knowing for certain that the addresses belong to the same owner. Potentially impossible depending on the tools/services used. I'm not saying Bitcoin is anonymous, it's not at all, the entire transaction history of every address is entirely visible to every man, and his dog. But it is pseudonymous if used correctly and that's what is important for your question. The funds can be traced through the addresses, but tying the owner to those addresses is what's important.

For example, note that this is not advice, but if you sent your identifiable purchased funds to an exchange, gambling site, dark net site, or other site that does not require ID verification. Then withdraw those funds in multiple transactions to different addresses in different wallets, using Tor or similar perhaps. Then those funds would be indistinguishable from the source funds in most cases. But, do your research if extreme privacy is important to you. Most of us are happy just pushing the funds through a simple mixer for a little bit of semi-privacy.