induction H.
unfold Par_strict in H.
spliter.
apply False_ind.
apply H2.
exists A.
split; Col.
spliter.
Col.
Qed.

Lemma per_diff : forall A B A' B' P, A <> B -> ~ Col A B A' ->
Per A A' P -> Per B B' P ->
A' <> P -> B' <> P -> A' <> B'.