scope.End ExtendInvariantIrr.f.
move=> nsHG sGD; rewrite inertia_morph_pre // morphim_setIpre.
by rewrite (setIidPr _) ?InerImplicit Types G H K L M N : {group gT}.End ConjBig.Section InertiaBigdprod.: {group gT}.
Hypothesis defG : \big[dprod/1%g]_(i | P i) A i = G.

(* Specifications: *)
by apply/bigcapP=> j /andP[/nAy]. Qed.