Section ORDERING.
(* B1 : If B is between A and C, then A, B, C are distinct points on a line, and also B is between C and A. *)
(* B2 : For any two distinct points A, B, there exists a points C such that B is between A and C. *)
(* B3 : Given three distinct points on a line, one and only one of them is between the other two. *)

Lemma B3a : forall A B C,
A <> B ->
B <> C ->
C <> A ->
Collinear A B C ->
Between A B C \/ Between B C A \/ Between C A B.