End Socle.
Section Clifford.
Variables (gT : finGroupType) (G H : {group gT}).
Hypothesis nsHG : H <| G.
Variables (n : nat) (rG : mx_representation F G n).
Let sHG := normal_sub nsHG.
Let nHG := normal_norm nsHG.
Let rH := subg_repr rG sHG.

Lemma Clifford_simple M x : mxsimple rH M -> x \in G -> mxsimple rH (M *m rG x).