We use this 'double' indication of possession with other words, not just names.
We cannot in English say *a Jack's friend, *a my father's friend, * a my friend. Instead we say: a friend of Jack's, a friend of my father's, a friend of mine.
There is a slight difference betweeen these two:
a friend of my father's - one of my father's friends
a friend of my father - her relationshiop with my father is that of being a friend.
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