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A corollary is a proof which is a direct result, or a direct application, of another proof.

It can be considered as being a proof for free on the back of a proof which has been paid for with blood, sweat and tears.

Linguistic Note

The word corollary is ultimately derived from the Latin corolla, meaning small garland, or the money paid for it.

Hence it also has the sense of something extra, lagniappe, freebie, a cherry on the top.