Fixpoint xfind (i j : key) (m : t A) : option A :=
match i, j with
| _, xH => find i m
| xO ii, xO jj => xfind ii jj m
| xI ii, xI jj => xfind ii jj m
| _, _ => None
end.

Lemma xelements_ih :
forall (m1 m2: t A) (o: option A) (i : key) (v: A),
List.In (xI i, v) (xelements (Node m1 o m2) xH) -> List.In (i, v) (xelements m2 xH).