Proof with intuition.
intros.
assert  {Y : Point | Col Y P Q /\ Col Y U V}.
apply inter_llex...
DecompExAnd H0 Y.
exists Y.
unfold inter_ll...
Qed.

Theorem on_parallel_ex : forall P Q R : Point,
Q<>R ->
~ Col P Q R ->
exists Y, on_parallel Y P Q R.