Hint Rewrite
pyth_simpl_1
pyth_simpl_2
py4_simpl_1
py4_simpl_2
py4_simpl_3
py4_simpl_4
py4_simpl_5
py4_simpl_6 : py_simplifications.
Ltac py_simpl := autorewrite with py_simplifications in *.

(* Specifications: *)
Lemma test_py_simpl : forall A B C, Py A A B = 0 -> Py A A B + Py B A A + Py4 B A C A = 0.
intros.