(** We show here that from the axioms of neutral geometry we can deduce the existence of a parallel line. This is important because it shows that axioms of neutral geometry are inconsistent with those of elliptic geometry as elliptic geometry assumes that no parallel lines exist. *)
(** This corresponds to l12_10 in Tarski's book. *)

Lemma line_dec : forall B1 B2 C1 C2, (Col C1 B1 B2 /\ Col C2 B1 B2) \/ ~ (Col C1 B1 B2 /\ Col C2 B1 B2).