"Complete disorder is impossible" T. Motzkin
Every large system contains a large well organized subsystem.
"How large" can be a great question (assuming we take it to mean large finite) but just showing that a certain class of systems has this property seems deeper to me. I find the audacity of the induction involved stunning. Sometimes the cleanest path to finite results is to replace "large" by "infinite", prove that result, and then concluded that the finite results hold. Some results are deep, in part, because we talk about sizes in ranges we need novel notation to even mention.