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 xfind_left :
forall (j i : key) (m1 m2 : t A) (o : option A) (v : A),
xfind i (append j (xO xH)) m1 = Some v -> xfind i j (Node m1 o m2) = Some v.