Since we are going to formalize constructive and predicative mathematics
in an intensional type theory like CIC, we try to establish some terminology.
-Type is the sort of sets equipped with the `Id `equality (i.e. an intensional,
+Type is the sort of sets equipped with the `Id` equality (i.e. an intensional,
not quotiented set). We will avoid using `Id` (Leibnitz equality),
thus we will explicitly equip a set with an equivalence relation when needed.
We will call this structure a _setoid_. Note that we will