Corollary Forall_sublist_first : forall {A} {d : Inhabitant A} (P : A -> Prop) i j l
  (Hrangei : 0 <= i <= Zlength l) (Hi : Forall P (sublist 0 i l)) (Hi' : ~P (Znth i l))
  (Hrangej : 0 <= j <= Zlength l) (Hj : Forall P (sublist 0 j l)) (Hj' : ~P (Znth j l)),
  i = j.

Lemma rotate_1 : forall v l n m, 0 <= n < m -> Zlength l < m -> rotate (upd_Znth 0 (complete m (v :: l)) (vptrofs 0)) n m = rotate (complete m l) ((n + 1) mod m) m.