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 index_of'_succeeds : forall k m i (Hi : 0 <= i < Zlength m) (Hnz : Forall (fun x => fst x <> 0 /\ fst x <> k) (sublist 0 i m)) (Hk : fst (Znth i m) = k \/ fst (Znth i m) = 0), index_of' m k = Some i.