I am pretty sure that either the TeXbook or Lesile Lamport's LaTeX users guide 
says \not is a slash with width 0 (and rather obviously ink outside it's 
official boundary). Whether that is the cleanest way to implement it in LyX is 
not a question I am qualified to comment on.

-- 
Duncan (-:
"software industry, the: unique industry where selling substandard goods is
legal and you can charge extra for fixing the problems."


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