apply perp_comm in H.
apply perp_perp_in in H.
assert(Per A B C).
apply perp_in_per.
Perp.
unfold Perp_at in H.
spliter.
intro.
subst C.
apply l8_8 in H0.
contradiction.
Qed.

(* Specifications: *)
Lemma per_preserves_bet_aux2 : forall P Q A B C A' C', P <> Q -> Bet A B C ->
Per A A' P -> Col P Q A' ->
Col P Q B ->
Per C C' P -> Col P Q C' ->
P <> A'-> P <> B -> P <> C' ->
Bet A' B C'.