Global Instance lcos_morphism :
 Proper (EqL ==> EqL ==> eq ==> iff) Lcos.

Lemma lcos_const_o : forall lp l a A B P, ~ Col A B P -> ~ Q_CongA_Null_Acute a -> Q_Cong l -> Q_Cong lp -> Q_CongA_Acute a -> l A B -> Lcos lp l a -> exists C, OS A B C P /\ a A B C /\ lp B C.