proposition: Lemma zx2qx_spec : forall P : QX, in_ZX P -> P [=] zx2qx (Q_can_num_poly P).
proof: Proof. intros P Hin. apply all_nth_coeff_eq_imp. intro n. set (Hin n). rewrite -> nth_coeff_zx2qx. rewrite -> (injZ_spec _ i). unfold inject_Z; simpl; unfold Qeq; simpl. rewrite Zmult_1_r, Zmult_1_r. symmetry; apply nth_coeff_Q_can_num_poly_spec. Qed.
imports: CPoly_Degree CoRN.model.rings.Qring Zring Qordfield CRing_Homomorphisms RingClass CRingClass Zlcm Q_can RX_deg