proposition: Lemma sqrt_to_nonneg : forall x, [0] [<=] x -> forall x2pos, sqrt (x[^]2) x2pos [=] x.
proof: Proof. intros. apply root_unique with 2. apply sqrt_nonneg. auto. auto. Step_final (x[^]2). Qed.
imports: CoRN.reals.OddPolyRootIR