... then the point is a false eye, and so White actually dies in gote. So White should not have played at a in the previous diagram after all.
here is a mistake. connects and lives. Note that at a is a common beginner mistake, know why?
If tries to capture , then cuts and we are back to a situation we have just seen. Now what happens when White captures the stone with a?
After captures the and stones, makes a throw-in, again reducing this eye to a false eye. We have seen this several times already, haven't we?
The White moves and here does not provide any form of resistance. After , all the Black stones connects out, and now if White plays at a, then Black b simply captures.