ite -row_full_dom_hom -!row_full_unit -!sub1mx => cGf nz.
by rewrite -[f]mul1mx irrG ?submx1 ?mxmodule1 ?mul1mx.
Qed.

(* Specifications: *)
Qed.
Qed.
Qed.
Local Notation rH := (subg_repr rG sHG).
Proof. by apply/setP=> x; rewrite !inE andbA -in_setI
End Stabilisers.
Qed.
Proof. by apply: mxsimple_subg; apply: mxmodule1. Qed.
Local Notation rH := (eqg_repr rG eqGH).
Proof. by rewrite rstabs_subg -(eqP eqGH) (setIidPr
End Stabilisers.
Qed.
Proof. exact: mxsimple_eqg. Qed.
Proof. by rewrite -rstabs_morphpre -(rstabs_subg _ sG_f'
Proof. exact: rfix_morphpre. Qed.
Qed.
Proof. exact: mxsimple_morphim. Qed.
Qed.
Proof. by rewrite -rker_submod rker_normal. Qed.
Qed.
Proof. exact: subset_trans rker_factmod. Qed.
Proof. by rewrite /mxmodule rstabs_conj. Qed.
Qed.