Proof with Geometry.
intros.
assert (~ Col Z B Y).
unfold not in |- *; intro.
unfold parallel in H3.
unfold S4 in H3.
assert (Col B Y Z)...
rewrite H5 in H3.
NormalizeRing H3...
assert (C <> B); eauto with Geom...
assert (Z <> Y); eauto with Geom...
apply l1_25_aux...
Qed.

(* Specifications: *)
Theorem thales :
forall S B C Z Y : Point,
~ Col C B Y ->
Col S B C ->
Col S Y Z ->
parallel Y B Z C-> Z <> Y ->
S ** B / C ** B = S ** Y / Z ** Y.