One of the great things about BTC is the reversibility of transactions. If you lose your private key, then your BTC are essentially destroyed because there is no way to access them.

My question is whether there is a way to INTENTIONALLY destroy BTC so that other users can tell that the supply of BTC has decreased? I realize that you could always claim to have destroyed the private key. But my question is whether there is any conceivable means of proving that to be true.