(** * Properties related to labels *)
(** If labels are globally unique and the Linear code [c] contains a subsequence [Llabel lbl :: c1], then [find_label lbl c] returns [c1]. *)
Fixpoint unique_labels (c: code) : Prop :=
match c with
| nil => True
| Llabel lbl :: c => ~(In (Llabel lbl) c) /\ unique_labels c
| i :: c => unique_labels c
end.

Lemma find_label_unique:
forall lbl c1 c2 c3,
is_tail (Llabel lbl :: c1) c2 ->
unique_labels c2 ->
find_label lbl c2 = Some c3 ->
c1 = c3.