Local Open Scope logic.
Instance LS: listspec t_struct_list _tail.
intros.
split; induction l1; intros.
inv H. destruct l2; inv H0. auto.
split. auto. simpl in H2. inv H2.
constructor; auto.
split. inv H. constructor; auto. apply IHl1 in H3.
intuition.
inv H. apply IHl1 in H3. intuition.
simpl. intuition.
simpl. constructor.
destruct H. inv H. auto.
apply IHl1. intuition.
inv H0; auto.
Qed.
Ltac destruct_ptr :=
match goal with
| [ H: isptr (?X) |- _] => let v := fresh "pt" in (remember X as v; destruct v; inv H)
end.

Lemma insert_insertion_sort : forall v l,
insert v (insertion_sort l) = insertion_sort (l ++ [v]).