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What if she refuses though after I pay to her? Is there a way to make it atomic and trustless?
What if she refuses after you pay to her on the current protocol (forget about LN)?In LN once two party will disagree then they can close the channel. The last balance of the balance-sheet which was successfully signed by the both party will be on count before the channel gets closed. And depending on the last balance of balance-sheet the bitcoin will be sent to both party.
There are no fraud for LN
update: Alice and Bob came from here?
https://youtu.be/rrr_zPmEiME