intros.
induction(eq_dec_points A A').
subst A'.
eapply proj_id.
4:apply H2.
3: apply H3.
auto.
Col.
assert(Col A C A').
eapply proj_eq_col.
apply H1.
assumption.
assert(Col A B A').
ColR.
eapply proj_id.
apply H4.
apply H6.
apply H1.
assumption.
Qed.

(* Specifications: *)
Lemma proj_diff_not_col : forall A B A' B' P Q, A <> A' -> proj A P Q A' -> proj B P Q B' ->  (A' <> B' <-> ~Col A B A').
intros.