Continuation error in Snape's memories?

Just to preface: I haven't read the books, I only have seen movies.

So in Harry Potter Deathly Hallows Part Two we see Snape's memories. In particular we see Snape cast a patronus (3:16). Now I wondering if it's a continuation error because in Half-Blood Prince, Dumbledore dies, but he's alive when Snape casts his Patronus which I'm assuming is the same Patronus that Harry sees in Deathly Hollows Part One. If that's the case then it's a continuation error or Snape made up this memory perhaps. Or is Snape casting a Patronus for a different situation that was in the books or another scene when Dumbledore was alive?