Section Cutting.
Variable A : Type.
Fixpoint firstn (n:nat)(l:list A) : list A :=
match n with
| 0 => nil
| S n => match l with
| nil => nil
| a::l => a::(firstn n l)
end
end.

Lemma firstn_app n:
forall l1 l2,
firstn n (l1 ++ l2) = (firstn n l1) ++ (firstn (n - length l1) l2).