toy theorem

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 illustrative and insightful to study proofs ofa toy theorem derived from a non-trivial theorem.Toy theorems also have a great education value.After presenting a theorem (with, say, a highly non-trivial proof),one can sometimes give some assurance that the theoremreally holds, by proving a toy version of the theorem.

For instance, a toy theorem of the Brouwer fixed point theoremis obtained by restricting the dimension to one.In this case, the Brouwer fixed point theorem followsalmost immediately from the intermediate value theorem(see http://planetmath.org/BrouwerFixedPointInOneDimensionthis page).