Corollary Znth_rebase' : forall {A} {d : Inhabitant A} (m : list A) i j, 0 <= i < Zlength m -> 0 <= j < Zlength m ->
  Znth ((i - j) mod Zlength m) (rebase m j) = Znth i m.

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