End JordanHolder.
Bind Scope irrType_scope with socle_sort.
Section Regular.
Variables (gT : finGroupType) (G : {group gT}).
Local Notation nG := #|pred_of_set (gval G)|.
Local Notation rF := (GRing.Field.comUnitRingType F) (only parsing).
Local Notation aG := (regular_repr rF G).
Local Notation R_G := (group_ring rF G).

Lemma gring_op_id A : (A \in R_G)%MS -> gring_op aG A = A.