(** If B is between A and C, it is also between C and A. *)

(* Specifications: *)
Lemma axiom_between_comm : forall A B C, Between_H A B C -> Between_H C B A.
Lemma axiom_between_out :
forall A B, A <> B -> exists C, Between_H A B C.
Lemma axiom_between_only_one :
forall A B C,
Between_H A B C -> ~ Between_H B C A.
Lemma between_one : forall A B C,
A<>B -> A<>C -> B<>C -> Col A B C ->
Between_H A B C \/ Between_H B C A \/ Between_H B 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.