Proof with Geometry.
intros.
assert (S C B Y = S Z B Y).
unfold parallel, S4 in H4.
assert (S B C Y = - S C B Y)...
rewrite H7 in H4.
RewriteVar (S C B Y) H4...
assert (S A B Y = S X B Y)...
assert (parallel B Y A X)...
unfold parallel, S4 in H8.
assert (S B A Y = - S A B Y)...
assert (S B Y X = S X B Y)...
rewrite H9 in H8.
rewrite H10 in H8.
RewriteVar (S A B Y) H8...
assert (A ** B / C ** B = S A B Y / S C B Y)...
assert (X ** Y / Z ** Y = S X B Y / S Z B Y)...
congruence...
Qed.

(* Specifications: *)
Theorem l1_25 :
forall A B C X Y Z : Point,
~ Col C B Y ->
Col A B C ->
Col X Y Z -> parallel A X B Y -> parallel B Y C Z ->
A ** B / C ** B = X ** Y / Z ** Y.