  Reynold's abstraction theorem is now a well-established result for a large
class of type systems. We propose here a definition of relational parametricity
and a proof of the abstraction theorem in the Calculus of Inductive
Constructions (CIC), the underlying formal language of Coq, in which
parametricity relations' codomain is the impredicative sort of propositions. To
proceed, we need to refine this calculus by splitting the sort hierarchy to
separate informative terms from non-informative terms. This refinement is very
close to CIC, but with the property that typing judgments can distinguish
informative terms. Among many applications, this natural encoding of
parametricity inside CIC serves both theoretical purposes (proving the
independence of propositions with respect to the logical system) as well as
practical aspirations (proving properties of finite algebraic structures). We
finally discuss how we can simply build, on top of our calculus, a new
reflexive Coq tactic that constructs proof terms by parametricity.
