(** This development is inspired by Theorem 32 of Hilbert's Foundations of Geometry (10th edition). It deduces completeness of a 2 or 3-dimensional space from completeness of lines. The original proof is due to Paul Bernays. *)
Section Completeness.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma line_completeness__completeness_for_3d_spaces :
(exists P Q R S, ~ Coplanar P Q R S) ->
line_completeness -> completeness_for_3d_spaces.