Original text:
(respectively _right subtree_). All trees used in this protocol are left-balanced binary trees.  A <del> binary tree is _full_ (and _balanced_) if it its size is a power of two and for any parent node in the tree, its left and right subtrees have the same size.  If a subtree is full and it is not a subset of any other full subtree, then it is _maximal_. </del>  A binary tree is _left-balanced_ if for every parent, either the parent is balanced, or the left subtree of that parent is the largest In order to update the state of the group such as adding and removing participants, MLS messages are used to make changes to the group's ratchet tree.  The participant proposing an update to the tree <del> transmits a representation of a set of tree nodes along the direct path from a leaf to the root.  Other participants in the group can use these nodes to update their view of the tree, aligning their copy of the tree to the sender's. </del>  To perform an update for a leaf, the sender transmits the following <del> information for each node in the direct path from the leaf to the root: </del>  The public key for the node <del> Zero or more encrypted copies of the node's secret value </del>  The secret value is encrypted for the subtree corresponding to the <del> node's non-updated child, i.e., the child not on the direct path. There is one encrypted secret for each public key in the resolution of the non-updated child.  In particular, for the leaf node, there are no encrypted secrets, since a leaf node has no children. </del>  The recipient of an update processes it with the following steps: Compute the updated secret values * Identify a node in the direct path for which the local participant is in the subtree of the non- <del> updated child * Identify a node in the resolution of the non- updated child for which this node has a private key * Decrypt the secret value for the direct path node using the private key from </del>  the resolution node * Compute secret values for ancestors of that node by hashing the decrypted secret This ciphersuite uses the following primitives: <del> Hash function: P-256 </del>  Diffie-Hellman group: secp256r1 (NIST P-256) 5.8. As described in ratchet-tree-updates, each MLS message needs to <del> transmit node values along the direct path from a leaf to the root. The path contains a public key for the leaf node, and a public key and encrypted secret value for intermediate nodes in the path.  In both cases, the path is ordered from the leaf to the root; each node MUST be the parent of its predecessor. </del>  The length of the "node_secrets" vector MUST be zero for the first node in the path.  For the remaining elements in the vector, the the removed leaf using the information in the Remove message Update the ratchet tree by setting to blank all nodes in the <del> direct path from the removed leaf to the root </del>  The update secret resulting from this change is the secret for the root node of the ratchet tree after the second step (after the third

Reviewer comments:
The very first commit from PR (6ba86ff561484a9eb96012e3b55b49f23cb8f9e9) was removed and a separate Issue is filled for unifying the use of "`" and "_".
We inconsistently use the backtick, the underscore or nothing for messages fields or specific operations in the draft. This needs a fix, currently the opinion is to use the TLS style (aka remove everything)

Revised text:
(respectively _right subtree_). All trees used in this protocol are left-balanced binary trees.  A  <ins> binary tree is _full_ (and _balanced_) if its size is a power of two and for any parent node in the tree, its left and right subtrees have the same size.  If a subtree is full and it is not a subset of any other full subtree, then it is _maximal_. </ins> A binary tree is _left-balanced_ if for every parent, either the parent is balanced, or the left subtree of that parent is the largest In order to update the state of the group such as adding and removing participants, MLS messages are used to make changes to the group's ratchet tree.  The participant proposing an update to the tree  <ins> transmits a set of values for intermediate nodes in the direct path of a leaf.  Other participants in the group can use these nodes to update their view of the tree, aligning their copy of the tree to the sender's. </ins> To perform an update for a leaf, the sender transmits the following  <ins> information for each node in the direct path of the leaf: </ins> The public key for the node  <ins> Zero or more encrypted copies of the node's parent secret value </ins> The secret value is encrypted for the subtree corresponding to the  <ins> parent's non-updated child, i.e., the child on the copath of the leaf node.  There is one encrypted secret for each public key in the resolution of the non-updated child.  In particular, for the leaf node, there are no encrypted secrets, since a leaf node has no children. </ins> The recipient of an update processes it with the following steps: Compute the updated secret values * Identify a node in the direct path for which the local participant is in the subtree of the non-  <ins> updated child * Identify a node in the resolution of the copath node for which this node has a private key * Decrypt the secret value for the parent of the copath node using the private key from </ins> the resolution node * Compute secret values for ancestors of that node by hashing the decrypted secret This ciphersuite uses the following primitives:  <ins> Hash function: SHA-256 </ins> Diffie-Hellman group: secp256r1 (NIST P-256) 5.8. As described in ratchet-tree-updates, each MLS message needs to  <ins> transmit node values along the direct path of a leaf.  The path contains a public key for the leaf node, and a public key and encrypted secret value for intermediate nodes in the path.  In both cases, the path is ordered from the leaf to the root; each node MUST be the parent of its predecessor. </ins> The length of the "node_secrets" vector MUST be zero for the first node in the path.  For the remaining elements in the vector, the the removed leaf using the information in the Remove message Update the ratchet tree by setting to blank all nodes in the  <ins> direct path of the removed leaf </ins> The update secret resulting from this change is the secret for the root node of the ratchet tree after the second step (after the third