PeterPeter wrote:So, if White does play inside the group, what is the procedure? Is the onus on White to prove he can live there, or on Black to prove he can kill?
To answer Peter's question directly, I believe the onus is on White to prove he can live there.
And since black can ignore most of the threats in this specific example, he can still play to actually capture the invading stones and come out ahead, in spite of losing point(s) to do so.
$$Wc black move 12 at a
$$ ---------------------------------------
$$ | . 0 9 1 3 5 7 a X . . . . . . . . . . |
$$ | X X X X X X X X X . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
- Click Here To Show Diagram Code
[go]$$Wc black move 12 at a
$$ ---------------------------------------
$$ | . 0 9 1 3 5 7 a X . . . . . . . . . . |
$$ | X X X X X X X X X . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |[/go]
Before the invasion, its (W:0, B:8, result 8-0 = B+8)
Since black can pass for moves 2,4,6 and 8, white is losing one point for each play (+4 to black). Black answers

with

(net zero: +1 to black, -1 from black). White must either pass or play elsewhere for 11, so Black now plays the otherwise unnecessary move

at a to capture 5 white stones (which I've already counted above as +5 to black; so net -1 to black)
B+8+4+0-1 = B+11
(black has 6 points of territory, and 5 white prisoners)
Black comes out ahead.
(
since no white territory has been displayed, instead of subtracting white's prisoners from white's score, algebraically we can just add them to black for the same score difference)