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Finality consists is declaring a block as irreversible. It is now forever part of the chain.
There exists two types of finality proofs: Grandpa commits, and Grandpa justifications. These two finality proofs are very similar to each other.
In order to be verified, both Grandpa commits and Grandpa justifications require that the verifier knows about specific block headers. Grandpa justifications directly include these block headers in its data, while Grandpa commits are sent in a context where it is assumed that they are known by the node.