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).