Corollary index_of_rebase : forall m n k, 0 <= n <= Zlength m -> NoDup (map fst m) ->
  index_of (rebase m n) k = option_map (fun i => (i - n) mod Zlength m) (index_of m k).

Lemma lookup_spec : forall m k (Hwf : wf_map m) (Hchain : well_chained m) (Hlen : Zlength m = size) (Hnz : k <> 0) (Hin : In k (map fst m)), lookup m k = index_of m k.