Definition irrType := socleType aG.
Identity Coercion type_of_irrType : irrType >-> socleType.
Variable sG : irrType.
Definition irr_degree (i : sG) := \rank (socle_base i).
Local Notation "'n_ i" := (irr_degree i) : group_ring_scope.
Local Open Scope group_ring_scope.

Lemma irr_degreeE i : 'n_i = \rank (socle_base i). Proof. by []. Qed.