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_at_sorted : forall v t p (Hp : find_leaf v t = Some p) (Hsorted : sorted (contents t)), exists t', insert_at v t p = Some t' /\ sorted (contents t').