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 complete_inj : forall l1 l2 m, complete m l1 = complete m l2 -> length l1 = length l2 -> l1 = l2.