Without loss of generality

Abstract

One sometimes reads in a mathematical proof that a certain assumption can be made 'without loss of generality' (WLOG). In other words, it is claimed that considering what first appears only a special case does nevertheless suffice to prove the general result. Typically the intuitive justification for this is that one can exploit symmetry in the problem. We examine how to formalize such 'WLOG' arguments in a mechanical theorem prover. Geometric reasoning is particularly rich in examples and we pay special attention to this area. © 2009 Springer.