Section Submodule.
Variables (gT : finGroupType) (G : {group gT}) (n : nat).
Variables (rG : mx_representation F G n) (U : 'M[F]_n) (Umod : mxmodule rG U).
Local Notation rU := (submod_repr Umod).
Local Notation rU' := (factmod_repr Umod).

Lemma rfix_submod (H : {set gT}) :
H \subset G -> (rfix_mx rU H :=: in_submod U (U :&: rfix_mx rG H))%MS.