Section vector_in.
Variable a : T.
Inductive vector_In : forall {n}, vector n -> Prop :=
| vHere : forall n rst, @vector_In (S n) (Vcons a rst)
| vNext : forall n rst b, @vector_In n rst ->
@vector_In (S n) (Vcons b rst).
End vector_in.

Lemma ForallV_vector_In : forall {n} t (vs : vector n) P,
ForallV P vs ->
vector_In t vs -> P t.