Toy theorem

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In mathematics, a toy theorem is a simplified version of a more general theorem. For instance, by introducing some simplifying assumptions in a theorem, one obtains a toy theorem.

Usually, a toy theorem is used to illustrate the claim of a theorem. It can also be insightful to study proofs of a toy theorem derived from a non-trivial theorem. Toy theorems can also have education value. 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.

For instance, a toy theorem of the Brouwer fixed point theorem is obtained by restricting the dimension to one. In this case, the Brouwer fixed point theorem follows almost immediately from the intermediate value theorem.