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.

In many scenarios, the use of "without loss of generality" is made possible by the presence of symmetry. For example, if some property P(x,y) of real numbers is known to be symmetric in x and y, namely that P(x,y) is equivalent to P(y,x), then