A corollary is a statement that follows naturally from some other statement that has either been proven or is generally accepted as true.
A corollary may be undeniably true if the concept or theory it's based on is true. For example, the sum of the interior angles of any triangle is always 180 degrees. One corollary to that theorem: Each interior angle of an equilateral triangle is 60 degrees.
However, corollaries are often considered accurate without being subjected to close scrutiny because they rely on the validity of the statements they are based on. The term is also used less stringently to refer to something that seems like it follows naturally from a statement that is considered true.
Some examples of corollaries:
Godwin's law states that if an online conversation goes on long enough, someone will almost certainly compare someone else to Hitler. A corollary to Godwin's law states that once that comparison has been made, the discussion is over because there is no point in continuing.
As originally stated, Murphy's law was "If there are two or more ways to do something, and one of those ways can result in a catastrophe, then someone will do it." Corollaries to Murphy's law are typically pessimistic refinements to the concept, such as, "if something is going to go wrong, it will happen at the time when it will do the most damage" and "if you foresee and prevent four potential disasters, a fifth possibility will present itself."
Parkinson's law maintains that the amount of work required for something will always increase so that it consumes any amount of time that may be allotted to it. One corollary to Parkinson’s law observes that, similarly, when the time available for a given task seems inadequate, the amount of work will decrease to hit a deadline. Parkinson's law of triviality, another corollary, observes that people often devote a lot of time to unimportant details while avoiding the crucial – and possibly more difficult – elements of a task.
According to broken window theory, every problem that goes unattended in a given environment affects people's attitude toward that environment and leads to more problems. A corollary to that theory maintains that well-tended environments are conducive to continued good management and maintenance.