(* Nats smaller than n *)
Fixpoint natsLess n : list nat :=
match n with
0 => []
| S n => n :: natsLess n
end.
(* Sum *)
Fixpoint sumn (A:list nat) :=
match A with
[] => 0
| a::A => a + sumn A
end.

Lemma sumn_app A B : sumn (A++B) = sumn A + sumn B.