Definition socle_repr W := submod_repr (socle_module W).

(* Specifications: *)
Lemma nz_socle (W : sG) : W != 0 :> 'M_n.
Lemma socle_mem (W : sG) : (W : 'M_n) \in socle_enum.
Canonical socle_subType := SubType _ _ _ socle_sort_rect PackSocleK.