Corollary rebase_upd' : forall {A} (m : list A) i j x, 0 <= i < Zlength m -> 0 <= j < Zlength m ->
  rebase (upd_Znth ((i + j) mod Zlength m) m x) j = upd_Znth i (rebase m j) x.

Lemma index_of'_upd2 : forall m k i k' v' (Hrange : 0 <= i < Zlength m) (Hi : index_of' m k <> Some i) (Hdiff : k' <> k /\ k' <> 0), index_of' (upd_Znth i m (k', v')) k = index_of' m k.