P=> Da nGa; rewrite !inE Da; apply/subsetP=> x Gx.
have Rx := subsetP sGR _ Gx; have Rxa: to x a \in R by rewrite gact_stable.
rewrite inE -sub1set -(injmSK injm_sdpair1) ?morphim_set1 ?sDefinition divgr A B x := x * (remgr A B x)^-1.Local Notation pprod := (partial_product gT).Local Notation sdprod := (semidirect_product gT) (only parsing).Local Notation cprod := (central_product gT) (only parsing).Local Notation dprod := (direct_product gT) (only parsing).Section ExtSdprodm.Notation "[ 'splits' B , 'over' A ]" := (splits_over B A)
  (at level 0, format "[ 'splits'  B ,  'over'  A ]") : group_scope.Definition xsdprodm := sdprodm (

Lemma mul0g : left_zero (@set0 gT) mulg.