Section Fold2.
Variable A B C: Type.
Variable f: A -> B -> C -> C.
Definition dhead a (l : list A) :=
match l with nil => a | b :: _ => b end.
Fixpoint fold2 (l1: list A) (l2: list B) (c: C) {struct l1}: C :=
match l1, l2 with
a::l3, b::l4 => fold2 l3 l4 (f a b c)
| _, _ => c
end.
Variable g: A -> B -> C.
Fixpoint map2 (l1: list A) (l2: list B) {struct l1}: list C :=
match l1, l2 with
a::l3, b::l4 => (g a b)::map2 l3 l4
| _, _ => nil
end.

Lemma map2_length l1 l2:
length (map2 l1 l2) = min (length l1) (length l2).