(* 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. *)

(* Specifications: *)
Lemma B4a : forall A B C M N,
~Collinear A B C ->
Between A M B ->
~Collinear A M N ->
~Collinear B M N ->
~Collinear C M N ->
(exists P : Point, Collinear M N P /\ Between A P C) \/
(exists P : Point, Collinear M N P /\ Between B P C).
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.