unfold proj in *.
spliter.
induction H2; induction H1; spliter.
apply col_permutation_1.
eapply perp2__col.
apply perp_sym.
apply perp_comm.
apply H5.
apply perp_sym.
Perp.
subst B.
Col.
subst C.
Col.
subst C.
Col.
Qed.

Lemma proj_par : forall A B A' B' P Q, A <> A' -> B <> B' -> proj A P Q A' -> proj B P Q B' -> Par A A' B B'.
intros.