Without loss of generality (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as without any loss of generality or with no loss of generality) is a frequently used expression in mathematics. The term is used before an assumption in a proof which narrows the premise to some special case; it implies that the proof for that case can be easily applied to all others, or that all other cases are equivalent or similar. Thus, given a proof of the conclusion in the special case, it is trivial to adapt it to prove the conclusion in all other cases.