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.
Lemma perp_1 : forall A B C D, perp A B C D -> perp A B D C.
Lemma perp_2 : forall A B C D, perp A B C D -> perp B A C D.
Lemma perp_3 : forall A B C D, perp A B C D -> perp B A D C.
Lemma perp_4 : forall A B C D, perp A B C D -> perp C D A B.
Lemma perp_5 : forall A B C D, perp A B C D -> perp C D B A.
Lemma perp_6 : forall A B C D, perp A B C D -> perp D C A B.
Lemma perp_7 : forall A B C D, perp A B C D -> perp D C B A.
Lemma perp_8 : forall A B C, perp A B B C -> per A B C.
Lemma perp_9 : forall A B C, per A B C -> perp A B B C.
Lemma not_eq_py_not_zero : forall A B, A<>B -> Py A B A <> 0.
Lemma py_zero_eq : forall A B, Py A B A = 0 -> A = B.