Section COMBINE.
Variables A B C: Type.
Variable f: option A -> option B -> option C.
Hypothesis f_none_none: f None None = None.
Fixpoint xcombine_l (m : t A) {struct m} : t C :=
match m with
| Leaf => Leaf
| Node l o r => Node' (xcombine_l l) (f o None) (xcombine_l r)
end.

Lemma xgcombine_l :
forall (m: t A) (i : positive),
get i (xcombine_l m) = f (get i m) None.