revert i j; induction v; intros i j Hi.
+ cbn; intros ? % divides_1_inv % not_qs_1; auto.
+ cbn; intros [ H % divides_pow | H  ] % divides_mult_inv; eauto.
* eapply primestream_divides in H; omega.
* eapply IHv in H; eauto.
Qed.

Lemma vec_prod_mult m v (u : pos m) i : @exp m i (vec_change v u (1 + vec_pos v u)) = qs (u + i) * exp i v.