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 test_uniformize_pys : forall A B C,
Py A B C - Py C B A + Py A A C + Py A C C + Py A B A - Py B A B = 0.