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.