Confusion with a definition in the Ethereum Yellow Paper

I am doing my undergrad thesis is on mathematically modeling blockchain systems. Can someone explain what is happening in this equivalent relationship?

As far as I understood, they defined sigma(a) as the account state and sigma(a)_s as the storageRoot hash of the Merkle trie that has all the account's storage data. L* is the collapse function that hashes all the key value pairs. So, I am guessing they are using the equivalent relationship to connect the Merkle Trie with the trie's root hash. But why is L* also taking the storageRoot hash?

https://preview.redd.it/m656e3k5qjod1.png?width=1080&format=png&auto=webp&s=7f308098e9a56dbf03e425db5ed2f29f83a63b30