Proof with Col.
unfold Perp,Perp_in.
intros.
DecompExAnd H0 X.
exists X.
repeat split;auto.
assert (Col A E X).
eapply col_transitivity_1;try apply H3...
Col.
intros.
apply H8.
assert (Col A B U).
eapply col_transitivity_1;try apply H...
Col.
Col.
Qed.
Hint Resolve perp_col : Perp.

(* Specifications: *)
Lemma perp_not_eq_1 : forall A B C D,
Perp A B C D -> A<>B.
Lemma perp_not_eq_2 : forall A B C D,
Perp A B C D -> C<>D.