Ltac uniformize_pys :=
repeat (rewrite pyth_simpl_1);
repeat (rewrite pyth_simpl_2);
repeat
match goal with
|  |- context [(Py ?A ?B ?C)] =>
(match goal with
|  |- context [(Py C B A)] => rewrite (pyth_sym A B C) in *
end)
|  |- context [(Py ?A ?B ?A)] =>
(match goal with
|  |- context [(Py B A B)] => rewrite (pyth_simpl_4 A B) in *
end)
end.

Lemma py4_7 : forall A B C D, Py4 A B C D = - Py4 D A B C.
Hint Resolve py4_1 py4_2 py4_3 py4_4 py4_5 py4_6 py4_7 : Geom.