Definition interp_CP {m : nat} (cp : cartesianPower positive (S m)) (interp: positive -> COINCpoint) : cartesianPower COINCpoint (S m).

(* Specifications: *)
Lemma interp_CPHdOK {m : nat} : forall (cp : cartesianPower positive (S m)) interp, interp_CP (headCPbis cp) interp = headCP (interp_CP cp interp).
Lemma interp_CPTlOK {m : nat} : forall (cp : cartesianPower positive (S (S m))) interp, interp_CP (tailCP cp) interp = tailCP (interp_CP cp interp).
Lemma interp_CPOK {m : nat} : forall (cp : cartesianPower positive (S m)) (interp: positive -> COINCpoint), CPToList (interp_CP cp interp) = map interp (CPToList cp).