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

Lemma lcos_per : forall A B C lp l a, Q_CongA_Acute a -> Q_Cong l -> Q_Cong lp -> Lcos lp l a -> l A C -> lp A B -> a B A C -> Per A B C.