(** [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 split_combine : forall (l: list (A*B)),
forall l1 l2, split l = (l1, l2) -> combine l1 l2 = l.