Jan Coenders' ship, the Graaf Willem

I had long thought that we didn't know the name of Jan Coender's ship. I noticed, however, upon a closer reading of The First Dutch War, that his ship was named the Graaf Willem. The passage called the ship a fluit. "De Sneuper" website, however, confirms what I had thought might be the case: the Graaf Willem was the Friese jacht. The obvious thought would be that this is the same Graaf Willem listed by Vreugdenhil, in his list from 1938. If so, then we know that the Graaf Willem carried 10 guns and was built in 1644. Her dimensions were: 74ft x 18.5ft x 7ft. I translated the text about Jan Coenders on "De Sneuper":

• 1653 Sea battle at Nieuwpoort 12/13 June, Captain Coenders on the yacht Graaf Willem
• On 11 July 1653, a courtmartial convicted Jan Coenders and found him unfit for further sea service. The verdict was signed by, among others, M. H. Tromp and M. A. de Ruyter.
• On 30 July Hessel Fransz. commanded the Graaf Willem, instead of Jan Coenders. Jan Coenders had been accused and convicted, but afterwards was rehired by the Friesland Admiralty.
• Battle near Wijk en Zee or Terheide, Jan Coenders commanded the yacht Graaf Willem. The ship was in a very bad state so that the guns fell through the moldy and rotten decks.