(** [combine] is the opposite of [split]. Lists given to [combine] are meant to be of same length. If not, [combine] stops on the shorter list *)
Fixpoint combine (l : list A) (l' : list B) : list (A*B) :=
match l,l' with
| x::tl, y::tl' => (x,y)::(combine tl tl')
| _, _ => []
end.

Lemma combine_split : forall (l:list A)(l':list B), length l = length l' ->
split (combine l l') = (l,l').