Ltac Perp := eauto with Perp.

(* Specifications: *)
Lemma l8_3 : forall A B C A',
Per A B C -> A<>B -> Col B A A' -> Per A' B C.
Lemma l8_4 : forall A B C C',
Per A B C -> is_midpoint B C C' -> Per A B C'.
Lemma l8_5 : forall A B, Per A B B.
intros.