(** * 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_add_branch: forall lbl k s, find_label lbl (add_branch s k) = find_label lbl k.