What is a Corollary in Mathematics?

Corollate is a term that is sometimes used in the context of mathematical proofs, particularly in the field of algebraic geometry. It is not a commonly used word, and it may not be familiar to many people.

In general, a corollary is a statement that follows logically from a previous statement, often as a consequence of a proof or a set of assumptions. In other words, a corollary is a secondary result that is derived from a primary result or theorem.

For example, if we have a theorem that states "If A then B", we might be able to deduce a corollary that says "If B then C". This means that the statement "C" logically follows from the statement "B", which in turn logically follows from the statement "A".

In practice, corollaries are often used to provide additional insight or to illustrate the consequences of a particular result. They can also be useful for helping to build a chain of logical arguments, where each step follows naturally from the previous one.