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

Lemma lcos3_exists : forall l a b c, Q_Cong l -> ~ Q_Cong_Null l -> Q_CongA_Acute a -> Q_CongA_Acute b -> Q_CongA_Acute c -> exists lp, Lcos3 lp l a b c.