Transaction overriding in lightning network I'm reading the lightning network whitepaper, and at some point it states this:


  Therefore, it is possible in bitcoin to devise a bitcoin script
  whereby all old transactions are invalidated, and only the new
  transaction is valid.


I would like to know the specifics of how this can be done. Seems to me that what they are describing here is some kind of transaction overriding? It is somewhat different from the mechanism I understood a micro payment channel works.
Lightning payment channels are established by two parties Alice and Bob paying into a 2-of-2 multisignature address. Concurrently, they create two "exit-transactions", one for each participant which pay out the current allotment of the payment channel, txAliceExit_1 and txBobExit_1. These exit transactions lock the fund of the executing party for some blocks.

When a payment is performed between Alice and Bob, they update the balance, create two new "exit-transactions", txAliceExit_2 and txBobExit_2. 

To invalidate the previous "exit-transactions" each party gives the counterparty another transaction that builds on the previous exit transaction by spending the party's output to the counterparty if the old "exit-transaction" were broadcast to the network, txAliceExit_1-TakeAll and txBobExit_1-TakeAll. I.e. if Bob executes txBobExit_1 the funds are time-locked for a little bit, meanwhile txAliceExit_1-TakeAll would become valid and Alice could take them before he can spend them.