An X-System is a function taking an X-System as input and outputting a boolean. Let X be the set of all such X-Systems
X: X -> Boolean
A T-System is an X-System which outputs true if the input is also a T-System, otherwise it outputs false. Let T be the set of all such T-Systems
T ⊆ X s.t. ∀ t ∈ T, x ∈ X, t(x) = x ∈ T