Definition all_equiv'_aux (l: list Prop) : Prop.
induction l; [exact True|].
induction l; [exact True|].
exact ((a -> a0) /\ IHl).
Defined.

(* Specifications: *)
Lemma all_equiv'_auxP : forall l n1 n2 d1 d2,
l <> nil -> all_equiv'_aux l ->
n1 < length l -> n2 < length l -> n1 <= n2 ->
nth n1 l d1 -> nth n2 l d2.