assert(Par A A' B B').
eapply (proj_par A B A' B' P Q); auto.
induction H4.
assumption.
spliter.
unfold Par_strict.
repeat split; auto; try apply all_coplanar.
intro.
ex_and H8 X.
assert(~Col P Q A).
eapply proj_not_col.
apply H.
assumption.
assert(~Col P Q B).
eapply proj_not_col.
apply H0.
assumption.
assert(A <> B).
eapply proj_not_eq.
apply H1.
apply H2.
assumption.
assert(Col A' P Q).
eapply proj_col.
apply H2.
assert(Col B' P Q).
eapply proj_col.
apply H3.
apply H1.
eapply (l6_21 P Q).
apply H11.
apply H0.
Col.
Col.
Col.
Col.
Qed.

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