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.

Lemma perp_per_1 : forall A B C, A<>B -> Perp A B C A -> Per B A C.