induction(eq_dec_points A B).
subst B.
Col.
unfold proj in *.
spliter.
induction H4; induction H5; spliter.
apply col_permutation_2.
eapply perp2__col.
apply perp_sym.
apply H6.
apply perp_left_comm.
eapply perp_col.
assumption.
apply perp_sym.
apply H8.
Col.
subst A'.
tauto.
subst B'.
Col.
subst B'.
Col.
Qed.

Lemma col_proj_proj : forall A B A' P Q, A <> A' -> Col A B A' -> proj A P Q A' -> proj B P Q A'.
intros.