In mathematics, a toy theorem is a simplified instance (special case) of a more general theorem, which can be useful in providing a handy representation of the general theorem, or a framework for proving the general theorem.
In many cases, a toy theorem is used to illustrate the claim of a theorem, while in other cases, studying the proofs of a toy theorem (derived from a non-trivial theorem) can provide insight that would be hard to obtain otherwise.
Toy theorems can also have educational value as well.
For example, after presenting a theorem (with, say, a highly non-trivial proof), one can sometimes give some assurance that the theorem really holds, by proving a toy version of the theorem.
This article incorporates material from toy theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.