intros...
assert (S4 A D C B = S4 B A D C)...
rewrite <- H...
Qed.
Hint Resolve S4_8: Geom.

(* Specifications: *)
Lemma lpar1 : forall A B C D : Point, parallel A B C D -> parallel A B D C.
Lemma lpar2 : forall A B C D : Point, parallel A B C D -> parallel B A C D.
Lemma lpar3 : forall A B C D : Point, parallel A B C D -> parallel B A D C.
Lemma ldiff : forall A B : Point, A <> B -> B <> A.
(***************************************************)
(* Simplification lemmas                           *)
(***************************************************)
Lemma simplring1 : forall x : F, x = - - x.
Lemma zeroegal : forall A B : Point, A = B -> A ** B = 0.
Lemma egalzero : forall A B : Point, A ** B = 0 -> A = B.
Hint Resolve zeroegal egalzero: Geom.
Lemma nuldirseg : forall A : Point, 0 = A ** A.
Lemma neq_not_zero : forall A B:Point,
A<>B -> A**B<>0.