The proverb Crosscut ? Then extend ( or The first to extend from a crosscut has the advantage) is somewhat misleading. There has been a lot of criticism that can be read at the /Technical Discussion page. A way to interpret the proverb is to reduce it to a not so common situation:
Some diagrams to explain.
An isolated cross-cut. Black to play.
It is tempting to play atari. Then connecting at is a good idea. However, this strengthens White and weakens the lone Black stone. A ladder at a may be possible.
After the more defensive-looking extension it is White's turn.
However White has to make a choice of her own which stone to strengthen. This is in fact an application of the 1-2-3 principle: if you are going to strengthen at in the previous diagram, why not do it at once as in this diagram.
Authors
Nobody seemed to object to my draft, so I replaced the old content of this proverb with the draft and moved the old content to a discussion page. --Dieter