unfold proj in *.
spliter.
induction H0; spliter; split; auto.
left.
repeat split.
intro.
apply H0.
Col.
Perp.
Col.
subst B.
right.
split; Col.
Qed.

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