How double spend is handled in lightning Network?

How double spend is handled in lightning Network?

How Lightning Network handles double-spend? What will happen when the other person is not available online to enforce the integrity of the transactions?

PFB my understanding of the Lightning Network.

Lightning Network builds an additional layer on top of the Bitcoin network that enables instant off-chain transfer of the ownership of the Bitcoin. Lightning Network utilises bi-directional payments channels that consist of multi-signature address.  Meaning Bitcoin will be held in a multi-signature address where transaction will use a multi-sign address as their input and point at two different address as their output. The transaction inside the lighting network are not broadcasted to the bitcoin network as long the channel is open(in order to reduce the load on the blockchain).

In this example how is Alice prevented from double spending?

  1. Alice and Bob both send 0.05 BTC into a shared 2-of-2 multisig address. This requires a transaction on the Bitcoin blockchain.

  2. Alice wants to pay 0.1 BTC to Bob. a. Alice creates a new transaction B2 and changes the balance to 0.4 BTC to Alice and 0.6BTC to Bob. b. Alice signs B2 and sends to Bob c. Now Bob creates a new transaction A2 and changes the balance to 0.4 BTC to Alice and 0.6BTC to Bob. d. Bob signs A2 and sends to Alice. After step 2a (before Bob verifies the transaction), can Alice close the channel and double spend the money?

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