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_not_two_sides_one_side_aux : upper_dim_axiom -> (forall A B X Y PX, A <> B -> PX <> A -> Perp A B X PX -> Col A B PX -> ~ Col X A B -> ~ Col Y A B -> ~ TS A B X Y -> OS A B X Y).