Clarity regarding deletion in a splay tree

Question

I am writing a code for splay tree but I have doubts regarding the deletion aspect of the splay tree. After researching about it on the internet, this is what I found:

First search the element to be deleted and splay it to the top.Then do the following

1. If the root (after splaying the element to the top) has both left and right child, delete the root such that you have now two subtrees.In the left subtree, find the largest element and splay it to the top and then connect it the root of the right subtree.
2. If the root has no left child but has a right child,then delete the root and make the root of the right subtree as the new root.

But what happens if the root has no right child? So I delete the root and make the root of the left subtree as the new root?

Are there any other conditions that I need to take care of?

If it helps, I have written the deletion code below.

def delete(self,key):
    res = self.get(key) #The get() function also does the splaying operation as well
    if res:
        ls = self.root.leftChild
        rs = self.root.rightChild
        if ls is not None and rs is not None: #has both the child
            ls.parent = None
            rs.parent = None
            current = ls
            while ls.hasRightChild():
                current = current.rightChild #find the largest element
            self.get(current.key)
            rs.parent = current
            current.rightChild = rs
            self.root = current
        elif ls is None and rs is not None: #has no left child
            rs.parent = None
            self.root = rs
        elif ls is None and rs is None: #has no left or right child ie the tree contains only one node
            self.root = None
    else:
        return