Definition eqopt (a b : option key) :=
match a, b with
| Some x, Some y => K.eq x y
| _ , _ => False
end.

Lemma searchtree_mid_congr:
forall c c' s1 x y s2 lo hi,
searchtree lo hi (T c s1 x s2) -> K.eq x y -> searchtree lo hi (T c' s1 y s2).