Merkle proof
Programming[1]
Merkle proofs are used to decide upon the following factors:
- If the data belongs in the merkle tree
- To concisely prove the validity of data being part of a dataset without storing the whole data set
- To ensure the validity of a certain data set being inclusive in a larger data set without revealing either the complete data set or its subset.
Merkle trees make extensive use of one way hashing. Merkle proofs are established by hashing a hash’s corresponding hash together and climbing up the tree until you obtain the root hash which is or can be publicly known. Given that one way hashes are intended to be collision free and deterministic algorithms, no two plaintext hashes can/should be the same.[2]
Video
This is a good description. Please stop watching this at 2:41 when he get's into implementation details.