[{"word":"corollaries","phonetics":[],"meanings":[{"partOfSpeech":"noun","definitions":[{"definition":"Something given beyond what is actually due; something added or superfluous.","synonyms":[],"antonyms":[]},{"definition":"Something which occurs a fortiori, as a result of another effort without significant additional effort.","synonyms":[],"antonyms":[],"example":"Finally getting that cracked window fixed was a nice corollary of redoing the whole storefront."},{"definition":"A proposition which follows easily from the proof of another proposition.","synonyms":[],"antonyms":[],"example":"We have proven that this set is finite and well ordered; as a corollary, we now know that there is an order-preserving map from it to the natural numbers."}],"synonyms":[],"antonyms":[]}],"license":{"name":"CC BY-SA 3.0","url":"https://creativecommons.org/licenses/by-sa/3.0"},"sourceUrls":["https://en.wiktionary.org/wiki/corollaries","https://en.wiktionary.org/wiki/corollary"]}]