demetria: It's hard to let go, but I think that's the only way to kill this formation. After White plays hane at , Black counters. This forms a partially filled bulky five. White sacrifices another stone at . After Black counters, then White can take the vital point.
Niklaus: I think you got the order wrong...
...Black is alive
demetria: If doesn't kill Black, then white should already see that and take to make Black's loss bigger; and then play the vital point if Black fails to do so.
So the correct solution is to make a dead shape first
demetria: I think Black would recognize this at and put a stop to it.
Black is canny enough to protect his territory (and we're trying to play white first). By making the hane (in the first diagram) you control black's reaction. Remember the rules for killing the eye: surround, reduce eyespace, take the vital point. Changing the order in this case allows Black to live (and to better advantage).
Also, at the top, if Black tries to play at , then with White's first move you have the ability to reduce Black to one false eye and then you kill the vital point in his three-point territory, so you can kill Black either way. Without the hane, Black has too many chances to make life.
Tyler: In this position Black is dead no matter whose move is next. Two eyes cannot be made from a square four in one move. White would have to follow a black move with a tenuki for Black to secure life.
demetria: Hold on a sec - let me fix four (I accidentally put 5). There. That looks a little different. Though it's best if Black takes the spot at first, and he's not sealed in so there's a slight chance of escaping.
Oh, I nearly forgot. Black's four-point space is only dead if Black is foolish enough the play inside of it first (and why would he do that?) White has to play inside it first. If White really wants to force the issue, then this happens:
White has a scant two liberties. Black ataris any move white makes. (This only works in the first diagram if White extends horizontally or vertically to give black a single eye.)
It seems that whoever plays first inside that particular space commits suicide.
Also in the first diagram, activity there on the right is going to be more urgent for Black, than capturing the three stones. He has no rush to get them because he can capture them any time he wants.