When you Mint a zerocoin, you spend a BTC. When you redeem a zerocoin, you receive a BTC. The collective of miners verifies that you don't get rich doing so.
But how do you know I just dont "sell it" to a btc address I already own? Or maybe I dont understand what you mean by spend BTC? Paid to who? The person "minting" coins, which is not a POW system?
The Mint transaction, which becomes part of the block chain, establishes consent that the given bitcoin address owns one BTC less and that simultaneously the given Zerocoin becomes valid.
Minting takes place within the block chain, unlike Dollar exchanges on MtGox, which are not directly visible as such in the block chain.
