assert (~ Col A B C -> ~ Col A C B).
intuition.
assert (~ Col A C B).
auto.
eapply notcolnotegal_1.
apply H1.
Qed.
Hint Resolve notcolnotegal_1 notcolnotegal_2 notcolnotegal_3: Geom.

Theorem notparallelnotegal_1 : forall A B C D,
~ parallel A B C D -> A<>B.