intros...
unfold parallel in H...
unfold S4 in H...
unfold not in |- *; intro...
assert (S P U Q = 0)...
rewrite H0...
assert (S P Q V = 0)...
rewrite H0...
rewrite H1 in H...
rewrite H2 in H...
Qed.

Theorem par_not_all_col :
forall P Q U V : Point, ~ parallel P Q U V -> ~ Col P U Q \/ ~ Col P Q V.