Require Export GeoCoq.Tarski_dev.Ch09_plane.
Section Upper_dim.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
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).