(** * Group II Order *)

(** Definition of the Between predicate of Hilbert.
    Note that it is different from the Between of Tarski.
    The Between of Hilbert is strict. *)

Definition Between_H := fun A B C =>
  Bet A B C /\ A <> B /\ B <> C /\ A <> C.

Lemma axiom_between_one : forall A B C, A<>B -> A<>C -> B<>C -> Col_H A B C -> Between_H A B C \/ Between_H B C A \/ Between_H B A C.