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Each transaction input has a key image, and there are around 2.1 inputs per transaction on average. So, the 'key image set' is around 2x the number of transactions on-chain. I do not believe a zero-knowledge proof is currently available, although you may find the description of a hypothetical 'unspent proof' in section 8.1.5 of Zero to Monero 2 is in the ...


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What is the exact size of the set of already spent key images and how it can be checked? Do we need to download the Monero blockchain to get the size? Yes, you'd need to download the blockchain. Once you have synced the blockchain, you can obtain the count of spent key images by inspecting the database like: mdb_stat -s spent_keys ~/.bitmonero/lmdb/ ... ...


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