(* The subspace fixed by a subgroup H of G; it is a module if H <| G.         *)
(* The definition below is extensionally equivalent to the straightforward    *)
(*    \bigcap_(x in H) kermx (rG x - 1%:M)                                    *)
(* but it avoids the dependency on the choice function; this allows it to     *)
(* commute with ring morphisms.                                               *)

Lemma rfix_mxP m (W : 'M_(m, n)) (H : {set gT}) :
reflect (forall x, x \in H -> W *m rG x = W) (W <= rfix_mx H)%MS.