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Currently Ethereum uses modified Merkle patricia trie and maybe plan to move to a sparse Merkle tree (SMT), which both support `proof of non-inclusion', i.e. allowing one to proof that some key does not stored in the data structure. Simple Merkle trees lack that feature. My question is why is this feature needed in Ethereum?

2

In some variations of plasma you need to prove that you didn't spend your balance.

For example if you want to exit a instance of plasma.

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