assert(~ Col A B C).
eapply per_not_col.
assumption.
assumption;
assert(Per B B' C).
eapply (l8_3 A); try auto.
Col.
assert(A <> B').
intro.
subst B'.
apply H5.
Col.
assert(Per A B B').
eapply (per_col _ _ C); auto.
Col.
assert(Per A B' B).
eapply (per_col _ _ C); auto.
Col.
eapply l8_7.
apply H7.
assumption.
Qed.

(* Specifications: *)
Lemma proj_one_side : forall A B A' B' P Q, A <> A' -> proj A P Q A' -> proj B P Q B' -> Col B A A' \/ OS A A' B B'.
intros.