So what he is doing is he is going to draw on prophecies from various places and remind them that this Jesus of Nazareth fit what those prophecies said, and so he begins with a resurrection. The Jews of that day would have recognized Psalm 16 as applying to the Messiah and applying to a resurrection of the Messiah. Now in verse 29 comes another part of the argument, because part of the argument might be, well, that psalm really did not apply to the Messiah, that psalm applied to David. Because he was generally seen to be the author of that psalm. And that maybe David was talking about himself. So he says,
His tomb was there. Now, how does that fit the context of Psalm 16? Well, it does not. He is implying, of course, that David went into the grave, into the tomb, and that David's body saw corruption. Therefore, he could not be the one being spoken about there. It had to be the Holy One of Israel. It had to be the Messiah that was being spoken of. So then David's tomb is proof that the psalmist was not writing about himself.
What did this tell the Jews? David's tomb still contained his body, and if that is the case, and Jesus' tomb is empty, and the great stone was rolled back and no one knows how that occurred, who then did this Psalm 16 refer to? It had to refer to David's greater Son - the Messiah, who was none other than Jesus of Nazareth, though a Galilean.