Definition Forall_tl (A : Type) (P : A -> Prop) (a : A) (l : list A)
           (H : Forall P (a :: l)): Forall P l.

Lemma nth_list_repeat' {A}: forall (a d:A) k i (Hik: (i <k)%nat), nth i (list_repeat k a) d = a.