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_P1 : forall (l:list R) (a:R), (0 < length l)%nat -> pos_Rl (a :: l) (length l) = pos_Rl l (pred (length l)).