Canonical pseries_group : {group gT} := group pseries_group_set.Local Notation ConsPred p := (@Cons nat_pred p%N) (only parsing).Implicit Types (A : {set aT}) (G H : {group aT}).

Lemma quotient_pseries_cat pi1s pi2s gT (G : {group gT}) : pseries (pi1s ++ pi2s) G / pseries pi1s G = pseries pi2s (G / pseries pi1s G).