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Help wanted with phrasing of rules (and their German translation.)

I have never been happy with the phrasing of the rule here (for example):

" Cells containing values exactly one greater than an immediate neighbor (diagonally or orthogonally) within their box are shaded. All the shaded cells are given. "

and I'd love to see your suggestions as to how it could be phrased more concisely, more precisely and generally more elegantly. As it stands I don't think it is even grammatical.

All suggestions welcome.

Meanwhile, it also strikes me that it would be polite if I provided a German translation of whatever rule is decided upon.

I'd suggest:

Ein schattiertes Feld enthält eine Zahl, die genau um eins größer ist als die in einem diagonal oder orthogonal benachbarten Feld. Ein unschattiertes Feld erfüllt diese Bedingung nicht.

Giving this to Google translate:

A shaded cell contains a number that is exactly one greater than that in a diagonally or orthogonally adjacent cell. An unshaded box does not meet this condition.
My suggestion:

If two (diagonally or orthogonally) neighboring cells within the same box contain consecutive numbers the cell with the higher number is shaded. All possible shaded cells are given.

I am not completely sure about my proposal but I post it for discussion purposes. I think that Dandelo's suggestion misses the "in the same box" constraint.
Thanks Dandelo and euklid.

There are elements that i like in each of your suggestions -- but it's really hard for me to tell -- I know what the rule is, so I find just about any expression of the rule comprehensible*. I'll leave the thread open for others to add their ideas/comments.

Perhaps in a few days if there are enough suggestions to justify it I could create a poll.

*indeed, the motivation for my post here is that a significant number of solvers find the rule as it is currently given difficult to parse.
I should have read it more carefully:

Ein schattiertes Feld enthält eine Zahl, die genau um eins größer ist als die in einem diagonal oder orthogonal benachbarten Feld in derselben 3x3-Box. Ein unschattiertes Feld erfüllt diese Bedingung nicht.

But the other suggestion is ok, too.
Thanks again, Dandelo and euclid. Both of your suggestions contain a kernel of good ideas. As it is I've recently changed "diagonally or orthogonally" to "diagonal or orthogonal" which somewhat improves the grammar.

If anyone finds the formulations proposed by Dandelo or euclid more appropriate, or have other ideas please comment.

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