I understand how bitcoins can be sent to a sidechain. The sidechain can be very main-bitcoin aware and validate that the bitcoins have been sent to a special type of side-chain address for that side chain. What I haven't been able to understand is how bitcoin can be returned back to the main chain, without bitcoin's main rules being explicitly aware of that sidechain (and validating it to receive the bitcoins onto the main chain again).

So how is this possible?