Without loss of generality
From AoPSWiki
Without loss of generality is a term used in proofs to indicate that an assumption is being made that does not introduce new restrictions to the problem. For example, in the proof of Schur's Inequality, one can assume that 
without loss of generality because the inequality is symmetric in 
, 
and 
. Without loss of generality is often abbreviated WLOG. Be sure not to write WLOG when you mean "with loss of generality"!
