Corollary insert_at_wf' : forall v p t t' (Hinsert : insert_at v t p = Some t')
      (Hwf : wf_btree t) (Hp : leaf_path t (removelast p)),
      wf_btree t' \/ wf_btree_over t'.

Lemma insert_sorted : forall v t t' (Hinsert : b_insert v t = Some t') (Hsorted : sorted (contents t)), sorted (contents t') /\ In v (contents t').