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

Lemma lcos2_lg_anga : forall lp l a b, Lcos2 lp l a b -> Lcos2 lp l a b /\ Q_Cong lp /\ Q_Cong l /\ Q_CongA_Acute a /\ Q_CongA_Acute b.