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Jun was the last king of Gija Joseon. He was succeeded by Wiman (Wei Man), whose usurpation of the throne began the dynasty of Wiman Joseon of Gojoseon.
Overthrowing and exile into Mahan
Wiman entered Gojoseon as a refugee, and submitted to King Jun. Jun granted Wiman's request to serve as a commander of the western borders. However, sometime around 194 BC or 193 BC, Wiman led a revolt, and followed Jun down into Mahan territory, which was situated in the southern part of the Korean Peninsula.
Peterson & Margulies 2009, p. 6: "The term was used again by a refugee from the Han dynasty named Wiman, who about 200 B.C.E. set up a kingdom in Korea called Wiman Choson."
Cotterell 2011, Imperial Crisis: The Failure of the Later Han: "The earliest documented event in Korean history involves China. After an unsuccessful rising against the first Han emperor Gaozu, the defeated rebels sought refuge beyond the imperial frontier and one of them Wiman, took control of Choson, a Korean state in the north of the peninsula."
Kim 2012, p. 10: "For instance, Wiman, a refugee from the Yan dynasty, which then existed around present-day Beijing, led his band of more than 1,000 followers into exile in Old Chosŏn in the early second century bc."
Tennant 1996, p. 18: "Retaliation by the Han then brought in refugees from Yan, the most notable of whom was a war lord, Weiman ('Wiman'in Korean), who somewhere about 200 BC led his followers into the territory held by Choson."
Xu 2007, p. 220: "Here, Wiman was described as a "Gu Yanren 故燕人"or a person from former Yan. It is confusing because there were two Yans around this period. The first was the Yan state, which was one of the seven states during the Warring States period, and the second was the vassal state of Yan of the Han dynasty."