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Related to double genitive: Genitive form
A phrasal construction in English in which possession is indicated by the word of followed by the possessive form of a noun or pronoun, as in a relative of mine or a friend of Pat's. Also called double possessive. See Usage Note at of.
a possessive construction consisting of a prepositional phrase with of containing a substantive in the possessive case, as of father's in She is a friend of father's. Also called double genitive.