Proof with Geometry.
intros.
assert (on_line_d Y P Q (P**Y/P**Q)).
apply on_line_to_on_line_d...
eapply elim_length_ratio_on_line_d_2...
apply H3.
Qed.

(* Specifications: *)
Lemma non_zero_denom_inter_ll_1_length_ratio :
forall A C D U V P Q Y : Point,
inter_ll Y P Q U V ->
S A U V <> 0 ->
parallel A Y C D ->
C <> D ->
S4 C U D V <> 0.