Section MorphPcore.
Implicit Types (pi : nat_pred) (gT rT : finGroupType).
Canonical pcore_igFun pi := [igFun by pcore_sub pi & morphim_pcore pi].
Canonical pcore_gFun pi := [gFun by morphim_pcore pi].
Canonical pcore_pgFun pi := [pgFun by morphim_pcore pi].
End PcoreMod.

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