A Merkle tree is a data structure for representing a key-value store as a tree. Each node of a Merkle tree is equipped with a hash value computed from those of their descendants. A Merkle tree is often used for representing a state of a blockchain system since it can be used for efficiently auditing the state in a trustless manner. Due to the safety-critical nature of blockchains, ensuring the correctness of their implementation is paramount. We show our formally verified implementation of the core part of Plebeia using F*. Plebeia is a library to manipulate an extension of Merkle trees (called Plebeia trees). It is being implemented as a part of the storage system of the Tezos blockchain system. To this end, we gradually ported Plebeia to F*; the OCaml code extracted from the modules ported to F* is linked with the unverified part of Plebeia. By this gradual porting process, we can obtain a working code from our partially verified implementation of Plebeia; we confirmed that the binary passes all the unit tests of Plebeia. More specifically, we verified the following properties on the implementation of Plebeia: (1) Each tree-manipulating function preserves the invariants on the data structure of a Plebeia tree and satisfies the functional requirements as a nested key-value store; (2) Each function for serializing/deserializing a Plebeia tree to/from the low-level storage is implemented correctly; and (3) The hash function for a Plebeia tree is relatively collision-resistant with respect to the cryptographic safety of the blake2b hash function. During porting Plebeia to F*, we found a bug in an old version of Plebeia, which was overlooked by the tests bundled with the original implementation. To the best of our knowledge, this is the first work that verifies a production-level implementation of a Merkle-tree library by F*.