Editing Consistency (section)

===Sketch of proof===
There are several things to verify. First, that <math>\sim</math> is in fact an equivalence relation.  Then, it needs to be verified that (1), (2), and (3) are well defined.  This falls out of the fact that <math>\sim</math> is an equivalence relation and also requires a proof that (1) and (2) are independent of the choice of <math> t_0, \ldots ,t_{n-1} </math> class representatives.  Finally, <math> \mathfrak I_\Phi \vDash \varphi </math> can be verified by induction on formulas.