Can you really prove that the last second really existed? I don't think so. It is like taking a frame from a movie reel and from that alone trying to prove that the previous frame really exist. You can't, there is always a possibility that it is the very first frame, or is just a photograph.

But does that stop you from claiming its existence (last second's)?

So as I said in another thread. This logic is completely ignoring the sea of subjective experience that we live in.