Fixpoint pos_Rl (l:list R) (i:nat) : R :=
  match l with
    | nil => 0
    | a :: l' => match i with
                     | O => a
                     | S i' => pos_Rl l' i'
                   end
  end.

Lemma pos_Rl_P2 : forall (l:list R) (x:R), In x l <-> (exists i : nat, (i < length l)%nat /\ x = pos_Rl l i).