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

Lemma l_25_b : forall A B P Q Y,
P<>Q -> Q<>Y -> Py Q A B <> 0 ->
on_inter_line_perp Y A P Q A B ->
P**Y / P**Q = Py P A B / Py4 P A Q B.