Global Instance independent_Tarski_neutral_dimensionless_follows_from_Hilbert :
  Gupta_inspired_variant_of_Tarski_neutral_dimensionless_with_decidable_point_equality.Global Instance H_to_T : Tarski_neutral_dimensionless.Global Instance H_to_T_PED :
  Tarski_neutral_dimensionless_with_decidable_point_equality H_to_T.

(* Specifications: *)
Lemma col_colh : forall A B C, Col A B C <-> ColH A B C.
Lemma bet__beth : forall A B C, A <> B -> B <> C -> Bet A B C -> BetH A B C.
Lemma coplanar_plane0 : forall A B C D X, ColH A B X -> ColH C D X -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
Lemma coplanar_plane1 : forall A B C D X, (Bet A B X \/ Bet B X A \/ Bet X A B) -> (Bet C D X \/ Bet D X C \/ Bet X C D) -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
Lemma coplanar_plane : forall A B C D, Coplanar A B C D -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
Lemma plane_coplanar : forall A B C D p, IncidP A p -> IncidP B p -> IncidP C p -> IncidP D p -> Coplanar A B C D.
Lemma pars__para : forall A B C D l m, IncidL A l -> IncidL B l -> IncidL C m -> IncidL D m -> Par_strict A B C D -> Para l m.
Lemma par__or_eq_para : forall A B C D l m, IncidL A l -> IncidL B l -> IncidL C m -> IncidL D m -> Par A B C D -> Para l m \/ EqL l m.