On August 8, 1425, Kim In-u was sent to "Muleungdo" to bring back people who had moved there illegally. After his return, on October 20, it was reported that one ship carrying 46 men was lost during the voyage. One month after that report was made, the following record mentions that the king ordered memorial services for the dead sailors.
Source: 『世宗實錄』 卷 三十, 世宗 七年 十一月 乙卯條
November 20, 1425
傳旨禮曹戶曹 茂陵入歸時敗船物故江原道船軍招魂致祭致賻 金麟雨云漂向日本 上以謂敗船 故有是命
예조와 호조에 전지(傳旨)하여, 무릉도(茂陵島)에 들어갈 때 배가 파손하여 사망한 강원도 선군(船軍)의 초혼제(招魂祭)를 지내어 치제(致祭)하고 치부(致賻)하게 하였다. 김인우(金麟雨)가 일본으로 표류(漂流)하였다고 말하였는데, 임금이 난파한 것이라 생각하였기 때문에 이러한 명령이 있은 것이다.
The king ordered the Ministry of Protocol and the Ministry of Finance to hold memorial services and pay condolences to honor the Kangwon Province sailors who died when their ship was destroyed while trying to land on Muleungdo. Kim In-u said that they had drifted to Japan, but the King gave the order because he thought they had been shipwrecked.
Muleungdo is the only island mentioned in the above record, but the record refers to Kim In-u, who was known as the Inspector for the Usan-Muleung Area, which suggests it was referring to his recent trip to the island.
I would like to take this opportunity to remind people that, so far, nothing has been mentioned in the records to suggest that either Usando or Muleungdo was a reference to present-day Dokdo/Takeshima. In fact, some records have said that both names referred to Ulleungdo, and other records have said that they are neighboring islands.
The fact that Kim In-u is referred to as the inspector for the Usan-Muleung "Area" instead of the Usan-Muleung "Island" suggests that the two are neighboring islands and not two names for one island. The fact that Usan is mentioned first implies that it is the larger island, but Muleungdo seems to be used more often when referring to the area, which makes things confusing. However, that confusion only reenforces the idea that the islands are near enough to each other to cause it.