intros...
unfold S4 in |- *...
assert (S A B C = S A B D + S A D C + S D B C)...
assert (S D B C = - S C B D)...
rewrite H0 in H...
assert (S A D C = - S A C D)...
rewrite H1 in H...
clear H0 H1...
rewrite H...
Qed.
Hint Resolve S4_1: Geom.

(* Specifications: *)
Lemma S4_2 : forall A B C D : Point, S4 A B C D = S4 B C D A.
Proof with try solve [ Geometry | ring ].