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].

Lemma pcore_char pi gT (G : {group gT}) : 'O_pi(G) \char G.