Definition Perp := fun A B C D => exists X, Perp_in X A B C D.

(* 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.
Lemma l8_6 : forall A B C A', Per A B C -> Per A' B C -> Bet A C A' -> B=C.