Hint Resolve perp_symmetry perp_commutativity perp_left_commutativity perp_right_commutativity : sPerp.
Hint Resolve perp_in_symmetry perp_in_commutativity perp_in_left_commutativity perp_in_right_commutativity : sPerp.
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.
Hint Resolve perp_per_1 perp_per_2 : Perp.
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.