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

Lemma lcos2_eq_trans : forall l1 a b l2 c d l3 e f, Eq_Lcos2 l1 a b l2 c d -> Eq_Lcos2 l2 c d l3 e f -> Eq_Lcos2 l1 a b l3 e f.