请教新概念英语中that of的用法

请教新概念英语中that of的用法
The mummy is that of Shepenmut who was once a singer in the Temple of Thebes.
这是新概念第二册,77课中的一个句子.
请邦我分析一下这个句子的结构,这个句子这样改写行不The mummy is Shepenmut who was once a singer in the Temple of Thebes.
也就是把that of删除掉了.
that of起什么作用呢?
还有这句
The operation,which lasted for over four hours,proved to be very difficult because of the hard resin which covered the skin.
这句可以这样改写么The operation proved to be very difficult because the hard resin which covered the skin.