are the corresponding combination of and . Additionally, there are sets of test equations. We can see that, by definition, all are constants. It is well-known in calculus that any derivative (full or partial) of any constant is . Hence, we can reduce each partial derivative to: and hence each term is zero, the left side each test equation is zero, each test equation is true, and the system is holonomic. Configuration spaces of two or one variable Any system that can be described by a Pfaffian constraint and has a configuration space or state space of only two variables or one variable is holonomic. We may prove this as such: consider a dynamical system with a configuration space or state space described as: if the system is described by a state space, we simply say that equals our time variable . This system will be described in Pfaffian form: with sets of constraints. The system will be tested by using the universal test. However, the universal test requires three variables in the configuration or state space. To accommodate this, we simply add a dummy variable to the configuration or state space to form: Because the dummy variable is by definition not a measure of anything in the system, its coefficient in the Pfaffian form must be . Thus we revise our Pfaffian form: Now we may use the test as such, for a given constraint if there are a set of constraints: Upon realizing that : because the dummy variable cannot appear in the coefficients used to describe the system, we see that the test equation must be true for all sets of constraint equations and thus the system must be holonomic. A similar proof can be conducted with one actual variable in the configuration or state space and two dummy variables to confirm that one-degree-of-freedom systems describable in Pfaffian form are also always holonomic. In conclusion, we realize that even though it is possible to model nonholonomic systems in Pfaffian form, any system modellable in Pfaffian form with two or fewer degrees of freedom (the number of degrees of freedom is equal to the number of terms in the configuration space) must be holonomic. Important note: realize that the test equation failed because the dummy variable, and hence the dummy differential included in the test, will differentiate anything that is a function of the actual configuration or state