Dokdo is already proved as Korean territory. Takeshima is a false name made by Japan.
Four types of evidence are needed for territorial verification: Historical,International legal, geographic,and effective evidence.Korea has all types of those evidence to prove that Dokdo is Korean territory.
First of all historical evidence. Dokdo was Korean territory since 513, when thae king of silla(Isabu) occupied Usanguk. According to the the Annals of the Joseon Dynasty, it is marked "After Isabu's occupation of Usanguk, Usanguk contributes to Silla's tribute of native products every year.
I gave some medicinal herbs and a few others on the Unsanguk."
Second, International legal evidence. "Dokdo belongs to the Ulleung County land, and Ulleung Island and a stone blade, Ulleung-gun, (Dokdo) govern."This is a part of 'Regulations of the republic of Korea No.41'. in 1900 whish is 5years earlier than the Japanese announcement in 1905.
Third, geographic evidence.Dokdo is visible for more than 30 days of the year when seen from Ulleung Island from over 80m.
Finally, effective evidence.Dokdo was a major sea lions, seals producer of the time , which proves that Dokdo is ulleungdo's sphere od living.