Ltac sPerp := eauto with sPerp.

(* Specifications: *)
Lemma perp_per_1 : forall A B C, A<>B -> Perp A B C A -> Per B A C.
Lemma perp_per_2 : forall A B C, A<>B -> Perp A B A C -> Per B A C.
Lemma perp_col : forall A B C D E, A<>E -> Perp A B C D -> Col A B E -> Perp A E C D.
Lemma perp_not_eq_1 : forall A B C D, Perp A B C D -> A<>B.
Lemma perp_not_eq_2 : forall A B C D, Perp A B C D -> C<>D.
Lemma perp_perp_in : forall A B C, Perp A B C A -> Perp_in A A B C A.