case: n => //; elim=> // n IHn g0T h0T H phi.
by rewrite !lcnSnsetIr D G)); case/derivedP=> n Gn1; apply/derivedP.
by exists n; rewrite /= -morphimIdom -morphim_der ?subsetIl // Gn1 morphim1.
Qed.

(* Specifications: *)
Canonical lcn_igFun n := [igFun by lcn_sub^~ n & lcn_cont n].