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 NoDup_Znth_inj : forall {A} {d : Inhabitant A} l i j (HNoDup : NoDup l) (Hi : 0 <= i < Zlength l) (Hj : 0 <= j < Zlength l) (Heq : Znth i l = Znth j l ), i = j.