proposition: Lemma nrootCC_1_ap_real : {z : CC | z[^]2 [=] a[+I*]b}.
proof: Proof. elim (ap_imp_less _ b [0]). intro H. exists (a'[+I*][--]b'). apply nrootCC_1_lower. assumption. intro H. exists (a'[+I*]b'). apply nrootCC_1_upper. assumption. assumption. Qed.
imports: CoRN.complex.CComplex Coq.Arith.Wf_nat Coq.setoid_ring.ArithRing