Section list_util.
Variables A B C : Type.
Hypothesis A_eq_dec : forall x y : A, {x = y} + {x <> y}.
Proof using.
intros l x H.
symmetry in H.
induction l;
now inversion H.
Qed.
Proof using.
induction xs; intros.
- intuition auto.
- simpl in *.
concludes.
break_or_hyp; break_if; subst; try congruence; intuition (auto with datatypes).
Qed.
Proof using.
induction xs; intros.
- auto.
- simpl in *. break_if; simpl in *; intuition auto.
Qed.
Proof using.
induction xs; intros; simpl; break_if; congruence.
Qed.
Proof using.
intros. induction xs; simpl in *; try break_if; intuition congruence.
Qed.
Proof using.
induction xs; intros.
- auto.
- simpl. rewrite IHxs. break_if; auto.
Qed.
Proof using.
induction xs; intros.
- auto.
- simpl. rewrite H by intuition (auto with datatypes).
rewrite IHxs by intuition (auto with datatypes). auto.
Qed.
Proof using.
induction xs; intros.
- constructor.
- simpl. invc_NoDup. constructor.
+ intro. do_in_map.
assert (x = a) by intuition (auto with datatypes).
congruence.
+ intuition (auto with datatypes).
Qed.

Lemma NoDup_disjoint_append :
forall (l : list A) l',
NoDup l ->
NoDup l' ->
(forall a, In a l -> ~ In a l') ->
NoDup (l ++ l').