Section Helpers.
Variable A : Type.
Fixpoint onth (s : seq A) n : option A :=
if s is x::sx then if n is nx.+1 then onth sx nx else Some x else None.
Definition prefix s1 s2 :=
forall n x, onth s1 n = some x -> onth s2 n = some x.
(* Lemmas *)

Lemma prefix_onth s t x : x < size s -> prefix s t -> onth s x = onth t x.