Remark diff_key1 :
forall (d : dict) (k k' : key) (v v' : data),
k <> k' -> occ v k (D_tree (add k' v' d)) -> occ v k (D_tree d).
Remark diff_key2 :
forall (d : dict) (k k' : key) (v v' : data),
k <> k' -> occ v k (D_tree d) -> occ v k (D_tree (add k' v' d)).

Theorem diff_key :
forall (d : dict) (k k' : key) (v : data),
k <> k' -> find k (add k' v d) = find k d.