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}).

(* Specifications: *)
Lemma morphim_pcore pi : GFunctor.pcontinuous (@pcore pi).
Lemma pseries_rcons pi pis gT (A : {set gT}) : pseries (rcons pis pi) A = pcore_mod A pi (pseries pis A).
Lemma pseries_subfun pis : GFunctor.closed (@pseries pis) /\ GFunctor.pcontinuous (@pseries pis).
Lemma pseries_sub pis : GFunctor.closed (@pseries pis).
Lemma morphim_pseries pis : GFunctor.pcontinuous (@pseries pis).
Lemma pseriesS pis : GFunctor.hereditary (@pseries pis).
Lemma quotient_pseries_cat pi1s pi2s gT (G : {group gT}) : pseries (pi1s ++ pi2s) G / pseries pi1s G = pseries pi2s (G / pseries pi1s G).
Lemma pseries_catl_id pi1s pi2s gT (G : {group gT}) : pseries pi1s (pseries (pi1s ++ pi2s) G) = pseries pi1s G.
Lemma pseries_catr_id pi1s pi2s gT (G : {group gT}) : pseries pi2s (pseries (pi1s ++ pi2s) G) = pseries pi2s G.
Lemma pseries_rcons_id pis pi gT (G : {group gT}) : pseries (rcons (rcons pis pi) pi) G = pseries (rcons pis pi) G.