intros.
unfold Py.
uniformize_dir_seg.
basic_simpl.
unfold not;intro.
apply H.
replace (A ** B * A ** B + A ** B * A ** B) with (2* A ** B * A ** B) in H0 by ring.
IsoleVar (A ** B ) H0...
replace (0 / A ** B / 2) with 0 in H0 ...
field...
Qed.
Hint Resolve not_eq_py_not_zero : Geom.

(* Specifications: *)
Lemma py_zero_eq : forall A B, Py A B A = 0 -> A = B.
Hint Resolve py_zero_eq : Geom.