That definition of trivial is not the one in regular usage.

A common joke in the mathematical community is to say that "trivial" is synonymous with "proved" — that is, any theorem can be considered "trivial" once it is known to be true. Another joke concerns two mathematicians who are discussing a theorem; the first mathematician says that the theorem is "trivial". In response to the other's request for an explanation, he then proceeds with twenty minutes of exposition. At the end of the explanation, the second mathematician agrees that the theorem is trivial. These jokes point out the subjectivity of judgments about triviality.

from http://en.wikipedia.org/wiki/Triviality_(mathematics)

Trivial doesn't mean easy. Just that it has been shown before or that new information won't be derived in the proof.