Section Sublist.
Inductive sublist (A : Type) : (list A) -> (list A) -> Prop :=
| sublist_refl : forall l, sublist l l
| sublist_skip : forall l1 h t, sublist l1 t -> sublist l1 (h :: t)
| sublist_cons : forall h t1 t2, sublist t1 t2 -> sublist (h :: t1) (h :: t2).
Hint Constructors sublist.

Lemma sublist_app_compat A (l1 l2 l3 l4 : list A) :
sublist l1 l3 ->
sublist l2 l4 ->
sublist (l1 ++ l2) (l3 ++ l4).