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

Lemma lcos3_eq_trans : forall l1 a b c l2 d e f l3 g h i, Eq_Lcos3 l1 a b c l2 d e f -> Eq_Lcos3 l2 d e f l3 g h i -> Eq_Lcos3 l1 a b c l3 g h i.