intros...
unfold S4 in |- *...
assert (S A C D = - S A D C)...
rewrite H.
assert (S A B C = - S A C B)...
rewrite H0.
ring.
Qed.
Hint Resolve S4_5: Geom.

Lemma S4_6 : forall A B C D : Point, S4 A B C D = - S4 D C B A.
Proof with try solve [ Geometry | congruence ].