Since double sente depends on the (global) positional context, examples ignoring it must be accompanied by an explanation of the made simplifying assumptions. One does not learn what double sente is by saying that it was double sente, period. And it really is not that hard for a book author to present a proper version of the example:
$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . . . . O . . . . O . X .
$$ | . . . X . , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------
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[go]$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . . . . O . . . . O . X .
$$ | . . . X . , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------[/go]
EDIT: oca,
$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . 2 . . O . . . . O . X .
$$ | . . . X 1 , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------
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[go]$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . 2 . . O . . . . O . X .
$$ | . . . X 1 , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------[/go]
Much later on the left lower side, this will be followed up by one of the following gote sequences:
$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . . 3 1 2 . . . . . . . .
$$ +----------------------------
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[go]$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . . 3 1 2 . . . . . . . .
$$ +----------------------------[/go]
$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . 2 1 3 . . . . . . . . .
$$ +----------------------------
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[go]$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . 2 1 3 . . . . . . . . .
$$ +----------------------------[/go]
For both together, one can imagine the simplifying average:
$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . . X O . . . . . . . . .
$$ +----------------------------
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[go]$$B
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . X . . O . . . . O . X .
$$ | . . . X O , . . . . . . . .
$$ | . . . X O . . . . . . . . .
$$ +----------------------------[/go]
Now compare this with
$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . . X . O . . . . O . X .
$$ | . . . X 1 , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . . X . O . . . . O . X .
$$ | . . . X 1 , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------[/go]
after which White has the sente / privilege follow-up
$$W 4 might also be at a, depending on global context
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . b X . O . . . . O . X .
$$ | . 4 a X O , . . . . . . . .
$$ | . . 2 1 3 . . . . . . . . .
$$ +----------------------------
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[go]$$W 4 might also be at a, depending on global context
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X . . . . O , . . . .
$$ | . . b X . O . . . . O . X .
$$ | . 4 a X O , . . . . . . . .
$$ | . . 2 1 3 . . . . . . . . .
$$ +----------------------------[/go]
Result: Black has lost 1 point in comparison to initially responding at b.
This is the pure local value explanation. However, b also makes better eyeshape and leaves behind fewer weaknesses for a white invasion if White should become even stronger around the corner. E.g., if Black can later invade the bottom, the white group there will become stronger and then b is in a better position. IOW, b is also the proper move and the better preparation for a possible black invasion.
Another consideration is this aji in case of Black's tenuki:
$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X 3 . . . O , . . . .
$$ | . . 2 1 . O . . . . O . X .
$$ | . . a X O , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------
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[go]$$W
$$ | . . . . . . . . . . . . . .
$$ | . . O . . . . . . . . . . .
$$ | . . . . . . . X . . X . . .
$$ | . . X . . . . . . . . . . .
$$ | . . . . . O . . . . . . . .
$$ | . . . X 3 . . . O , . . . .
$$ | . . 2 1 . O . . . . O . X .
$$ | . . a X O , . . . . . . . .
$$ | . . . . . . . . . . . . . .
$$ +----------------------------[/go]
Usually a is the attacking move, but White can also create this ko.