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_ii :
forall (m: t A) (i j : key) (v: A),
List.In (xI i, v) (xelements m (xI j)) -> List.In (i, v) (xelements m j).