(** * 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_diff :
forall A B C, Between_H A B C -> A<>C.