corollary
a theorem that can be proved easily using another theorem
A corollary is a proposition that follows very readily from previous statements or from something that has already been proved. It is essentially a logical consequence of what has been stated or proven already. In mathematics, corollaries are often used to derive a result that is important or useful for the problem at hand. For instance, if we prove a theorem that X implies Y, then a corollary of that theorem could be that NOT Y implies NOT X. The corollary is a direct consequence of the original theorem and it helps us to further understand the relationship between X and Y. In general, corollaries are a way of extending the implications or consequences of a statement or result that has already been established.
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