Definition cut' A B X Y := X <> Y /\ forall l, IncidL X l -> IncidL Y l -> cut l A B.
Global Instance cut_morphism : Proper(EqL ==> eq ==> eq ==> iff) cut.

Lemma ColH_bets : forall A B C, ColH A B C -> Bet A B C \/ Bet B C A \/ Bet C A B.
Global Instance independent_Tarski_neutral_dimensionless_follows_from_Hilbert :
Gupta_inspired_variant_of_Tarski_neutral_dimensionless_with_decidable_point_equality.