In my research I came across a case where I could derive a known theorem with rather straightforward way by choosing "non-standard" definitions using my knowledge from a related field. This particular case does not seem to be interesting to wider audience, but I would expect that there are cases where the real crux is in the definitions and the later deductions are just "the necessity" to establish some results. Good definitions do, after all, "compress" prior knowledge in a succinct form and often make the following work easy.

This motivates to ask if there are concrete examples where the real progress is in the definitions and the following (potentially interesting) results are just illustration of the power of the definition(s)?

isdefinitions.... – Thompson Mar 2 '17 at 20:26