intros.
intro.
subst B'.
apply H0.
eapply per2__col.
apply H1.
assumption.
assumption.
Qed.

Lemma per_preserves_bet : forall P Q A B C A' B' C', P <> Q -> Bet A B C ->
Per A A' P -> Col P Q A' ->
Per B B' P -> Col P Q B' ->
Per C C' P -> Col P Q C' ->
P <> A'-> P <> B' -> P <> C' ->
Bet A' B' C'.