Loss of generality

In mathematics, without loss of generality (WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is used to indicate the assumption that what follows is chosen arbitrarily, narrowing the premise to a particular case, but does not affect the validity of the proof in general. The other cases are sufficiently similar to the one presented that proving them follows by essentially the same logic. As a result, once a proof is given for the particular case, it is trivial to adapt it to prove the conclusion in all other cases.