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)).