End Completeness.
(** In the following sections, we prove that our formalizations of Hilbert's axiom of completeness are always true in spaces with dimension respectively greater than 2 and 3. *)
Section Dimension.
Context `{Tn:Tarski_neutral_dimensionless}.

Lemma nupper_dim__completeness_for_planes : ~ upper_dim_axiom -> completeness_for_planes.