intros.
simpl in |- *.
red in |- *.
intro i.
unfold restricted_seq in |- *.
unfold const_map in |- *.
simpl in |- *.
apply Refl.
Qed.
Hint Resolve const_map_restricted: algebra.

Lemma restricted_seq_preserves_distinct :
forall (A : Setoid) (n m : Nat) (v : seq n A) (H : m <= n),
distinct v -> distinct (restricted_seq v H).