Ltac cases_per A B C := elim (per_dec A B C);intros.

Lemma l3_5_py : forall A B U V Y,
U <> V ->
Col Y U V ->
Py A Y B = U**Y / U**V * Py A V B + Y**V/ U**V * Py A U B
- (U**Y/ U**V) * (Y**V / U**V) * Py U V U.