Variables (S : predPredType R) (addS : addrPred S) (kS : keyed_pred addS).

(* Specifications: *)
Lemma polyOverP {p} : reflect (forall i, p`_i \in kS) (p \in polyOver kS).
Lemma polyOverC c : (c%:P \in polyOver kS) = (c \in kS).
Fact polyOver_addr_closed : addr_closed (polyOver kS).