Definition upper_dim_axiom := forall A B C P Q : Tpoint,
  P <> Q -> Cong A P A Q -> Cong B P B Q -> Cong C P C Q ->
  (Bet A B C \/ Bet B C A \/ Bet C A B).Definition all_coplanar_axiom := forall A B C D, Coplanar A B C D.

Lemma upper_dim_implies_col_perp2__col : upper_dim_axiom -> (forall A B X Y P, Col A B P -> Perp A B X P -> Perp P A Y P -> Col Y X P).