Section HilbertContext_2D.
Context `{H2D : Hilbert_neutral_2D}.

Lemma col_upper_dim : forall A B C P Q,
ColH A P Q -> P <> Q -> A <> B -> A <> C -> B <> C ->
A <> P -> A <> Q -> B <> P -> B <> Q -> C <> P -> C <> Q ->
CongH A P A Q -> CongH B P B Q -> CongH C P C Q ->
(Bet A B C \/ Bet B C A \/ Bet C A B).