Do blocks contain their nonce and target?

I have just watched the basic lectures on proof of work. It wasn’t said explicitly in the lecture, but don’t blocks have to contain their nonce and the target? If they didn’t, it seems like other nodes in the network would not be able to verify that a new block found a valid nonce. I guess the point is that the nonce can’t be just some number they use once and then forget, because then verification would be impossible.

The nonce is stored in the block header, obviously it has to be stored or the block would have to be remined every time.