py_simpl.
ring.
Qed.

(* Specifications: *)
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.