Definition Perp_tagged A B C D := Perp A B C D.

(* Specifications: *)
Lemma Perp_Perp_tagged : forall A B C D, Perp A B C D -> Perp_tagged A B C D.
Lemma Perp_tagged_Perp : forall A B C D, Perp_tagged A B C D -> Perp A B C D.