corollary
a direct or natural consequence or result
In mathematics, a corollary refers to a statement that follows readily from a previously proven proposition. The corollary does not require additional proof since it is considered to be a direct consequence or result of the original proposition.
Corollaries are often used to extend the application and understanding of the original proposition. For example, suppose the original proposition states that if a is greater than b and b is greater than c, then a is greater than c. A corollary of this proposition could be if x, y, and z are three different positive integers, then x+y+z is greater than x+y and y+z.
Corollaries can help mathematicians save time and effort by allowing them to refer to previously proven statements without having to provide a full proof again. They also help to showcase the interconnectedness of different mathematical concepts.
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