Proof with Geometry.
intros.
unfold inter_ll in *.
DecompAndAll.
apply (elim_length_ratio_on_line_2 A C D U V Y)...
unfold on_line.
split...
unfold not;intro;subst U...
Qed.
(* TODO A<>Y has been added check that implementation takes care of it *)

Lemma non_zero_denom_inter_ll_2_length_ratio :
forall A C D U V P Q Y : Point,
inter_ll Y P Q U V ->
S A U V = 0 ->
C<>D ->
A<>Y ->
parallel A Y C D ->
S4 C P D Q <> 0.