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_simpl_3 : forall A B C, Py4 A B A C = 0.