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. *)
(* B4 : (Pasch). Let A, B, C be three noncollinear points, and let L be a line not containing any of A, B, C. If L contains a point D lying between A and B, then it must contain either a point lying between A and C or a point lying between B and C, but not both. *)

Lemma B4b : forall A B C M N P Q,
~Collinear A B C ->
Between A M B ->
~Collinear A M N ->
~Collinear B M N ->
~Collinear C M N ->
Collinear M N P ->
Between A P C ->
Collinear M N Q ->
Between B Q C ->
False.